The image distance is 60 cm if An object is placed 30 cm from the diverging mirror has a focal length of 20cm.
What is diverging mirror ?A concave mirror, also known as a converging mirror, has an inwardly recessed reflecting surface (away from the incident light). Concave mirrors focus light inward to a single focal point. They are used to concentrate light. Concave mirrors, unlike convex mirrors, produce different image types depending on the distance between the object and the mirror.
The mirrors are referred to as "converging mirrors" because they collect light that falls on them and refocus parallel incoming rays toward a focus. This is due to the fact that light is reflected at different angles at different spots on the mirror due to the fact that the normal to the mirror surface varies at each spot.
use mirror formula
[tex]\frac{1}{f}[/tex] = [tex]\frac{1}{v}[/tex] + [tex]\frac{1}{u}[/tex]
The image distance is 60 cm
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The ratio of diameter of lenses to its focal length is referred as
The ratio of diameter of lenses to its focal length is referred as the f-number or f-stop
The ratio of diameter of lenses to its focal length is referred to as the f-number or f-stop. It is a fundamental parameter that describes the aperture of a lens, which determines the amount of light that can pass through the lens. The f-number is calculated by dividing the focal length of the lens by the diameter of the aperture, which is the opening that controls the amount of light entering the lens.
A smaller f-number indicates a larger aperture, which allows more light to enter the lens, resulting in a brighter image and a shallower depth of field. Conversely, a larger f-number indicates a smaller aperture, which allows less light to enter the lens, resulting in a darker image and a greater depth of field.
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Calculate the fuel efficiency of a vehicle that can travel 350 km using 20l of gasoline include units in your answer
What is the distance between two spheres, each with a charge of 1. 05 X 10^-7 C when the force between them is 0. 40 N?
Answer:
Answer:please mark as brainliest
(PLS HELP ME NOW!!!!!) Ospreys are birds that eat fish. Where would an osprey MOST likely live?
A.
near a forest
B.
near a marsh
C.
near a desert
D.
near a prairie
Meadow voles are small mouse-like animals that eat plants and insects. Their niche in an ecosystem is a
A.
omnivore.
B.
herbivore.
C.
producer.
D.
scavenger.
Answer:
B. herbivore.
Explanation:
Meadow voles primarily consume plants, such as grasses, herbs, and bark, although they may also eat insects occasionally. As a result, their niche in an ecosystem is that of a herbivore, which is an organism that consumes primarily plants.
If it takes 726 watts of power to move a mass 36 meters in 14 seconds, then what is the magnitude of the object’s mass?
A. 12. 1 kg
B. 20. 2 kg
C. 28. 8 kg
D. 282 kg
When an item must be moved 36 meters in 14 seconds using 726 watts of electricity, its mass is 28.8 kg.(c) is the right option.
Any quantity in mechanics may be defined in terms of mass, length, length time. The letter m stands for kilogram, which represents mass in the SI. Contrary to popular belief, relativistic mass must always be thought of when moving at speeds that are near to the lightest possible speed.
The Power is provided with p = 726 watt.
The Time is 14 seconds.
d = 36 m is the distance traveled.
Use the provided formula to calculate power.
p = W / t
p = m * g * h / t (w = m * g * h)
726 = m * 9.8 * 36 / 14 ( g = 10 m/s^2)
m = 28. 8kg.
As a result, the object's mass 36 m in 14 s equals 28.8 kg even when an item needs 726 watts of electricity to move it.
The mass of it as an item, a key indication of the volume of both the thing's contents, is used to calculate its inertia, a fundamental attribute. Descriptions of weight might appear circular because it's such a fundamental concept and difficult to express in words of every other concept.
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calculate the minimum coefficient of friction needed for a car to negotiate an unbanked 50.0 m radius curve at 30.0 m/s. (b) what is unreasonable about the result? (c) which premises are unreasonable or inconsistent?
A-the minimum coefficient of friction is 0.18 ,B- it is unreasonable, C-no premises is inconsistent.
(a) Calculation of the minimum coefficient of friction needed for a car to negotiate an unbanked 50.0 m radius curve at 30.0 m/s: A car moving with a velocity of 30.0 m/s in a circular path of radius 50.0 m negotiates an unbanked curve. Hence, the force required to move a car in a circular path is the frictional force between the wheels of the car and the road.
The minimum coefficient of friction needed for a car to negotiate an unbanked 50.0 m radius curve at 30.0 m/s is given by:μmin = tanθ= v² / rgWhere,μmin is the minimum coefficient of frictionv is the velocity of the carr is the radius of the curveg is the acceleration due to gravity θ is the angle of banking.
As the curve is unbanked, the angle of banking is 0°.∴ μmin = v² / rg= (30.0 m/s)² / (50.0 m × 9.81 m/s²)= 0.183 or 0.18 (approx)
(b)The result of 0.18 is not unreasonable.
(c) None of the premises is unreasonable or inconsistent.
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A harmonic wave travels in a wire with amplitude 2. 51 mm, wavelength 1. 09 m, and frequency 649 Hz. What is the speed with which the wave travels
The speed of a harmonic wave traveling in a medium is given by the product of its wavelength and frequency, i.e.,
v = λ f, where v is the velocity of the wave, λ is the wavelength, and f is the frequency. In this case, the given amplitude of the wave is not needed to calculate the speed. We can simply use the wavelength and frequency provided to find the velocity. Substituting the given values, we get: v = (1.09 m) × (649 Hz) = 706.41 m/s. Therefore, the speed with which the wave travels is 706.41 m/s. Note that the unit of velocity in SI is meters per second (m/s).
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Is the earth round? Or is it flat like some people say
Answer: The Earth is an oblate spheroid, meaning it is roughly spherical in shape but flattened at the poles and bulges at the equator. This shape has been scientifically proven through centuries of evidence and observations. While some people may claim that the Earth is flat, this idea is not supported by scientific evidence.
. Is it possible to make a steel bar into a magnet? If so, explain
the method.
Answer:
yes if you can only install a magnetic force into the bar
Question 2
2 pts
A 76 kg person is sledding down a hill is traveling at 20 m/s when they hit a stationary 20 kg person and they end up both riding together in the
sled. How fast will they be moving together immediately after they collide?
The speed of the sled and the two people immediately after the collision is approximately 15.8 m/s.
What is the Law of conservation of momentum?The conservation of momentum, which states that the total momentum of a closed system remains constant if no external forces act on it. In this case, the sled and the two people form a closed system, because there are no external forces acting on them.
Let's define the initial state as before the collision, and the final state as after the collision. In the initial state, the sled and the 76 kg person have a momentum of:
p1 = (76 kg)(20 m/s) = 1520 kg·m/s
The second person is stationary, so their momentum is zero:
p2 = 0 kg·m/s
The total momentum before the collision is therefore:
p1i = p1 + p2 = 1520 kg·m/s + 0 kg·m/s = 1520 kg·m/s
In the final state, the two people and the sled move together with a common velocity, which we'll call v. The total mass of the system is:
m = 76 kg + 20 kg = 96 kg
The total momentum after the collision is:
p1f = m v
By the conservation of momentum, the total momentum before the collision must be equal to the total momentum after the collision:
p1i = p1f
1520 kg·m/s = 96 kg × v
Solving for v, we get:
v = 1520 kg·m/s / 96 kg ≈ 15.8 m/s
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A converging lens forms a real image of an object. if magnification is 2 and the distance between the image and the object is 90.0cm; determine the
(i) Focal length of the lens
(ii) Distance for which the image would be the same size as the object.
(I) The focal length of the lens is 180.0 cm.
(II) The distance for which the image would be the same size as the object is 90.0 cm.
What is the focal length of the lens?We can use the lens equation and the magnification formula to solve for the focal length of the lens and the distance for which the image would be the same size as the object.
The lens equation is:
1/f = 1/do + 1/di
where;
f is the focal length of the lens, do is the distance between the object and the lens, and di is the distance between the image and the lens.We are given that the distance between the image and the object is 90.0 cm and the magnification is 2. The magnification formula is:
m = - di/do
where;
m is the magnification.Substituting these values into the magnification formula, we get:
2 = - di/do
di = -2do
Substituting these values into the lens equation, we get:
1/f = 1/do - 1/2do
Simplifying this equation, we get:
1/f = 1/2do
f = 2do
Substituting the given value of di, we get:
f = 2(-90.0 cm) = -180.0 cm
Since the focal length must be positive for a converging lens, we take the absolute value and get:
f = 180.0 cm
(ii) Distance for which the image would be the same size as the object:
When the image is the same size as the object, the magnification is 1. We can use the magnification formula to solve for the distance di:
m = - di/do
1 = - di/do
di = -do
Substituting the given value of do, we get:
di = -90.0 cm
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two objects having masses m 1 and m 2 are connected to each other as shown in the figure and are released from rest. there is no friction on the table surface or in the pulley. the masses of the pulley and the string connecting the objects are completely negligible. what must be true about the tension t in the string just after the objects are released?
The tension T in the string just after the objects are released must be equal and opposite to the accelerations of each mass.
The statement refers to a physical principle known as Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
In the context of the given statement, it means that the tension (T) in the string, which is the force transmitted through the string, must be equal in magnitude and opposite in direction to the accelerations of each mass.
When objects are released and allowed to move under the influence of gravity, they may be connected by a string or rope. As the objects accelerate due to the force of gravity, the tension in the string changes to keep the objects connected and moving together.
According to Newton's third law, the tension in the string must be equal and opposite to the accelerations of each mass.
If one of the objects has a greater acceleration, the tension in the string must be higher on that side to counteract the greater acceleration.
Similarly, if one of the objects has a lower acceleration, the tension in the string must be lower on that side. This ensures that the net force on each object is balanced and that they move together without breaking the string.
This is because Newton's Second Law states that the sum of the forces on an object is equal to the mass times the acceleration: F = ma. Therefore, the tension T must be the same for both masses, since their accelerations must be equal and opposite.
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Calculate the ideal mechanical advantage for each of the machines show. Write your answers in the spaces provided.
For Machine 1 ideal mechanical advantage is 4, for machine 2 the IMA is 8 and for the machine 3 the IMA is 4. The load the machines can lift is 400N, 800N and 200N respectively.
The ideal mechanical advantage of a machine is an important factor in determining its efficiency and usefulness. The higher the IMA, the easier it is to lift heavy loads with less effort. However, it is important to note that the actual mechanical advantage (AMA) may differ from the ideal due to various factors such as friction and other mechanical losses. Therefore, it is essential to consider both IMA and AMA when evaluating the performance of a machine.
Machine 1:
Ideal Mechanical Advantage (IMA) = Load / Effort
IMA = 400 N / 100 N
= 4
Machine 2:
IMA = Load / Effort
IMA = 800 N / 100 N
= 8
Machine 3:
IMA = Load / Effort
IMA = 200 N / 50 N
= 4
In simple terms, the ideal mechanical advantage (IMA) of a machine is the ratio of the load it can lift to the effort or force needed to lift it. In other words, it is the number of times a machine multiplies the force or effort applied to it.
For Machine 1, the IMA is 4, which means that the machine can lift a load that is four times heavier than the applied force. Therefore, if you apply 100 N of force to the machine, it can lift a load of up to 400 N.
For Machine 2, the IMA is 8, which means that it can lift a load that is eight times heavier than the applied force. If you apply 100 N of force to this machine, it can lift a load of up to 800 N.
For Machine 3, the IMA is 4, which means that it can lift a load that is four times heavier than the applied force. If you apply 50 N of force to this machine, it can lift a load of up to 200 N.
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What will be the final velocity of a car, if it starts to move from rest and accelerates at 10 m/s² after 5 seconds ?
Answer:
50m/s.
Explanation:
Answer:
[tex]V_f=50m/s[/tex]
Explanation:
Use the the formula for final velocity (kinematic equation):
[tex]V_f=V_i+at[/tex]
Final velocity = Initial velocity + acceleration times time
Given values:
Rest - indicates 0 initial velocity
Acceleration - 10 m/s^2
Time - 5 seconds
Insert the given values:
[tex]V_f=0+5\times10[/tex]
[tex]V_f=50m/s[/tex]
The distance traveled by an object per unit time is called
The distance an object travels in a unit of time is called the speed of the object. SI. the unit of speed is meter per second (ms−1).
Speed is measured in relation to distance compared to the time it took to cover the distance. Speed is a scalar quantity because it only has direction and not magnitude. There are four types of speeds and they are:
Even speed
Variable speed
Average speed
Instantaneous speed
Constant velocity: An object is at a constant velocity when the object travels the same distance in equal intervals of time.
Variable speed: an object is said to have variable speed when the object travels varying distances at regular intervals.
Average speed: Average speed is defined as the constant speed obtained by the ratio of the total distance traveled by the object to the total time spent on the object. Instantaneous velocity: When an object is moving with a variable velocity, the velocity of that object at any instant of time is called instantaneous velocity.
Speed measurement
A speedometer is used to measure the speed of vehicles. An odometer is used to measure the distance traveled. Speed can also be calculated using a gragraphph. A distance-time graph helps to understand the speed of an object.
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A boat float on the surface of the lake sends a signal summer force vertically down to the water the sooner trace is 0. 007 sand the speed of sound is 1,500m/s. How deep is the water?
A boat float on the surface of the lake sends a signal summer force vertically down to the water the sooner trace is 0. 007 sand the speed of sound is 1,500m/s. 21 meters deep is the water.
The time it takes for the sound wave to travel from the boat to the bottom of the lake and back is given by:
t = 2d/v
Where:
d = depth of the water
v = speed of sound in water (1,500 m/s)
We can solve for d by rearranging the equation as:
d = v × t/2
Where:
t = the time it takes for the sound wave to travel from the boat to the bottom of the lake and back, which is equal to twice the time it takes for the sound wave to travel from the boat to the bottom of the lake.
The time it takes for the sound wave to travel from the boat to the bottom of the lake is given by:
t = d/v
Where:
d = distance traveled by the sound wave (which is equal to the depth of the water)
v = speed of sound in water (1,500 m/s)
We can substitute this expression for t into the equation for d to get:
d = v × d/2v
Simplifying this expression, we get:
d/0.007 = 2 × 1500
d = 21 meters
Therefore, the depth of the water is approximately 21 meters.
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Police radar guns (Figure 1) work by measuring the change in frequency of a reflected pulse of electromagnetic waves. A gun reads correctly only if a car is moving directly toward or away from the person making the measurement.
The following are the answers to the following questions:
There will not be a Doppler shift.
There will still be a Doppler shift observed by the radar gun.
What exactly is Doppler shift?Doppler shift is the change in frequency of a wave caused by relative motion between the source and the observer. This shift in frequency can be used to calculate the relative motion of the source and observer and is employed in a variety of applications such as radar, astronomy, and medical imaging.
1: The guns are adjusted for forward or backward motion towards or away from the gun. What happens if an automobile moves perpendicular to the gun's line of sight?
The radar gun will not detect any Doppler shift.
2: If the car is approaching or departing from a different angle, there is .
A Doppler change will still be detected, but it will be less than the maximum Doppler shift that would occur if the car moved directly towards or away from the gun.
3: As a result, if the radar gun indicates that a car is driving at a specific speed, the car is moving at the speed radar report.
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You use a rope and pulley system with an ideal mechanical advantage of 2.00. How big of an output load can you lift with an input
force of 200 N?
When two rope segments pull up on the load in the single movable pulley, the optimal mechanical advantage is 2. This sort of pulley does not change the direction of the applied force, but it does increase it by a factor of two.
What is the ideal mechanical advantage?There are two methods for calculating a pulley system's mechanical advantage.
The mechanical advantage may be calculated simply by counting the number of falls (or active lifting ropes) that are really attached to the load. You may also split the effort distance by the load distance.
Assuming an ideal rope and pulley system with a mechanical advantage of [tex]2.00[/tex] , the output load that can be lifted with an input force of [tex]200 N[/tex] can be calculated using the formula:
Output force = Input force x Mechanical advantage
Where the mechanical advantage is given as [tex]2.00[/tex] .
Thus, the output force is:
Output force [tex]= 200 N \times 2.00 = 400 N[/tex]
Therefore, with an input force of [tex]200 N[/tex] , the rope and pulley system can lift an output load of up to [tex]400 N[/tex] .
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Please help. I do not know what to do
1) The heat is 10,800 J
2) The heat is 2400 J
3) The time is 100 s
What is the heating effect of current?The heating effect of current, also known as Joule heating or resistive heating, is a phenomenon where electrical energy is converted into heat when an electric current flows through a material that has resistance.
1) We know that;
H = I^2rt
H = (3)^2 * 4 * 5 * 60
H = 10,800 J
2) H = (V^2/R)t
H = (10)^2/5 * 2 * 60
H = 2400 J
3) H =(V^2/R)t
t = H/(V^2/R)
t = H * R/V^2
t = 4 * 10^3 * 10/20^2
t = 100 s
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calculate the magnitude of the linear momentum for the following cases: (a) a proton with mass equal to 1.67 3 10227 kg, moving with a speed of 5.00 3 106 m/s; (b) a 15.0-g bullet moving with a speed of 300 m/s; (c) a 75.0-kg sprinter running with a speed of 10.0 m/s; (d) the earth (mass 5 5.98 3 1024 kg) moving with an orbital speed equal to 2.98 3 104 m/s.
To calculate the magnitude of the linear momentum for each of the cases, you need to use the following equation:
Linear momentum (p) = mass (m) x velocity (v)
Case (a): Linear momentum (p) = 1.67 x 10-27 kg x 5.00 x 106 m/s = 8.35 x 10-22 kg m/s
Case (b): Linear momentum (p) = 0.015 kg x 300 m/s = 4.5 kg m/s
Case (c): Linear momentum (p) = 75.0 kg x 10.0 m/s = 750 kg m/s
Case (d): Linear momentum (p) = 5.98 x 1024 kg x 2.98 x 104 m/s = 1.78 x 1029 kg m/s
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can you explain how he got 60/11 please! , i got boards tomorrow grade 10 . deciding to sit and study till morning :(!
The position of the image of the object would be 7.5 cm behind the mirror.
Position of the image of objects in a mirrorThe focal lengths of all convex mirrors are negative and are given by the following formula:
1/f = - (1/R)
where:
R is the radius of curvature of the mirror.Substituting for R in the equation, we are going to have:
1/f = -1/20 cm
f = -20 cm
Next, we can make use of the mirror formula to find the position of the image along the plane of the mirror:
The mirror formula goes thus:
1/f = 1/do + 1/di
where 'do' is the object distance and di is the image distance.
Substituting the values of f and di:
1/-20 cm = 1/12 cm + 1/di
Thus:
di = -7.5 cm
That the di is negative is an indication that the image is a virtual one that forms behind the mirror. In other words, the position of the image is 7.5 cm behind the mirror.
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Explain the stages of complete and incomplete metamorphosis, provide examples for each. (Counts 20% of your lesson grade.)
Metamorphosis refers to the process of development and change in the body form of certain animals as they grow from juveniles to adults.
Explain the types of metamorphosis?
Metamorphosis is classified into two types: complete and incomplete.
1. Complete metamorphosis:
Complete metamorphosis is a developmental process in which the juvenile form of an animal goes through four distinct stages: egg, larva, pupa, and adult. In this type of metamorphosis, the juvenile form looks completely different from the adult form in terms of appearance, behavior, and habitat.
Animals that undergo complete metamorphosis include:
a) Butterflies and moths: The egg hatches into a caterpillar (larva) that feeds and grows rapidly. The larva then forms a pupa or chrysalis, where the body undergoes a complete transformation into an adult butterfly or moth.
b) Flies: The egg hatches into a worm-like maggot (larva) that feeds and grows. The maggot then transforms into a pupa, and finally, an adult fly emerges.
c) Beetles: The egg hatches into a grub (larva) that feeds and grows. The grub then transforms into a pupa, and finally, an adult beetle emerges.
Incomplete metamorphosis:
Incomplete metamorphosis is a developmental process in which the juvenile form (nymph) of an animal resembles the adult in appearance and habitat, but is smaller and lacks wings. The nymph goes through several stages of growth and molting before reaching adult form.
Animals that undergo incomplete metamorphosis include:
a) Grasshoppers: The egg hatches into a nymph that resembles the adult grasshopper but lacks wings. The nymph goes through several molts and growth stages before developing wings and reaching the adult stage.
b) Cockroaches: The egg hatches into a nymph that resembles the adult cockroach but lacks wings. The nymph goes through several molts and growth stages before developing wings and reaching the adult stage.
c) Dragonflies: The egg hatches into a nymph that lives in water and resembles the adult dragonfly but lacks wings. The nymph goes through several molts and growth stages before developing wings and emerging from the water as an adult dragonfly.
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an 80 kg person weighs himself on a planet having a radius of 2500 km and finds that the scale shows 75 n.calculate the mass of planet.
The mass of the planet is approximately [tex]7.87 x 10^23 kg.[/tex]
We can use the formula for the gravitational force between two masses:
[tex]F = G * (m1 * m2) / r^2[/tex]
where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them. In this case, the person's weight on the planet is equal to the force of gravity between the person and the planet: F = 75 N. The person's mass is 80 kg, so their weight on Earth would be:
[tex]W = m * g = 80 kg * 9.8 m/s^2 = 784 N[/tex]
We can set these two forces equal to each other and solve for the mass of the planet: [tex]75 N = G * (80 kg * m_planet) / (r_planet)^2\\[/tex]We can rearrange this equation to solve for the mass of the planet:
[tex]m_planet = (75 N * (2500 km)^2) / (G * 80 kg)\\[/tex]
where[tex]G = 6.674 x 10^-11 N*m^2/kg^2[/tex]is the gravitational constant.
Plugging in the values, we get: m_planet = [tex](75 N * (2500 km)^2) / (6.674 x 10^-11 N*m^2/kg^2 * 80 kg)[/tex]
m_planet = [tex]7.87 x 10^23 kg[/tex]
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How can scientists detect a black hole if it does not emit light?
How much energy is required to melt 64g of methane of 90K ? (methane is 16 g/ mol)
Answer:
12.928 kJ
Explanation:
To calculate the energy required to melt a substance, we use the formula:
Q = m * ΔHfus
where Q is the energy required, m is the mass of the substance, and ΔHfus is the heat of fusion, which is the amount of energy required to melt one gram of the substance.
For methane, the heat of fusion is 0.202 kJ/g. We can calculate the amount of energy required to melt 64g of methane as follows:
Q = m * ΔHfus
Q = 64g * 0.202 kJ/g
Q = 12.928 kJ
Therefore, it takes approximately 12.928 kJ of energy to melt 64g of methane at 90K.
What process involves heavier atoms breaking down into lighter atoms?
Answer:
Fission occurs when a neutron slams into a larger atom, forcing it to excite and split into two smaller atoms—also known as fission products. Additional neutrons are also released that can initiate a chain reaction. When each atom splits, a tremendous amount of energy is released.
Explanation:
Answer:
Fission
Explanation:
this happens when the neutrons an atoms slams into a larger atom, forcing it to split into two smaller atoms
A Saturn
V
rocket's powerful boosters are capable of producing a powerful upward acceleration of
11.7 m/s 2
. During a test run of a similar rocket, NASA launches a prototype vertically upward on a calm day (no wind), burning fuel and producing a roughly constant acceleration until it reaches an upward speed of
679 m/s
. After the engines shut off, the rocket begins to freefall, eventually coming back down to the earth after reaching a maximum height of
42.3 km
. Ignoring air resistance, a) How far from the ground was the rocket when its boosters turned of and it began to freefall? b) What was the prototype rocket's upward acceleration while its boosters were firing? c) For how long were the boosters firing? d) For what total time is the rocket in the air before striking the ground?
The correct answer for a) the rocket was 19,671.65 meters (or 19.67 km) from the ground when the boosters turned off, b) rocket's upward acceleration while its boosters were firing was 11.7 m/s^2, c) the boosters were firing for 58.04 seconds, d) the rocket is in the air for a total of 199.38 seconds
a) To find the distance from the ground when the boosters turned off, we can use the formula for displacement in terms of initial velocity, acceleration, and time:
d = v_i*t + 0.5*a*t^2
We know the initial velocity (v_i) is 0 m/s, the acceleration (a) is 11.7 m/s^2, and the final velocity (v_f) is 679 m/s.
We can use the formula v_f = v_i + a*t to find the time (t) that the boosters were firing:
679 m/s = 0 m/s + 11.7 m/s^2 * t
t = 58.04 s
Now we can plug this time into the displacement formula:
d = 0 m/s * 58.04 s + 0.5 * 11.7 m/s^2 * (58.04 s)^2
d = 19,671.65 m
So the rocket was 19,671.65 meters (or 19.67 km) from the ground when the boosters turned off.
b) The prototype rocket's upward acceleration while its boosters were firing was 11.7 m/s^2, as given in the question.
c) As calculated in part a), the boosters were firing for 58.04 seconds.
d) To find the total time the rocket is in the air, we need to find the time it takes to reach its maximum height and the time it takes to fall back to the ground.
We can use the formula d = v_i*t + 0.5*a*t^2 again, with the initial velocity (v_i) being 679 m/s, the acceleration (a) being -9.8 m/s^2 (due to gravity), and the displacement (d) being the difference between the maximum height and the height when the boosters turned off:
42.3 km - 19.67 km = 22.63 km = 22,630 m
22,630 m = 679 m/s * t + 0.5 * -9.8 m/s^2 * t^2
Solving this quadratic equation gives us two solutions for t, but only one is positive:
t = 70.67 s
So the time it takes to reach the maximum height is 70.67 seconds.
The time it takes to fall back to the ground is the same, since the initial and final velocities are the same but in opposite directions. Therefore, the total time the rocket is in the air is:
t_total = 58.04 s + 70.67 s + 70.67 s = 199.38 s
So the rocket is in the air for a total of 199.38 seconds before striking the ground.
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a roller-coaster car is towed up an incline at a steady speed of 0.500 m/s by a chain parallel to the surface of the incline. the slope is 3.00%, which means that the elevation increases by 3.00 m for every 100.0 m of horizontal distance. the mass of the roller-coaster car is 604 kg. ignoring friction, what is the magnitude of the force exerted on the car by the chain?
A roller-coaster car is towed up an incline at a steady speed of 0.500 m/s by a chain parallel to the surface of the incline. the slope is 3.00%. ignoring friction, the magnitude of the force exerted on the car by the chain is: 5908.7 N
The magnitude of the force exerted on the roller-coaster car by the chain is equal to the net force on the car, which is equal to the sum of the force due to gravity and the force due to the incline. Since the roller-coaster car is moving at a steady speed, the net force on the car must be equal to zero.
Using Newton's second law of motion, we can calculate the force due to gravity (Fg) and the force due to the incline (Fi) in order to determine the magnitude of the force exerted on the car by the chain.
The force due to gravity (Fg) can be calculated as Fg = m * g, where m is the mass of the roller-coaster car and g is the acceleration due to gravity. Therefore, Fg = 604 kg * 9.8 m/s2 = 5902.8 N.
The force due to the incline (Fi) can be calculated as Fi = m * g * sinθ, where m is the mass of the roller-coaster car, g is the acceleration due to gravity, and θ is the angle of the incline. The angle of the incline is equal to the slope of the incline divided by 100. Therefore, θ = 3.00% / 100 = 0.03 radians.
Therefore, [tex]Fi = 604 kg * 9.8 m/s2 * sin(0.03) = 5.9 N.[/tex]
Therefore, the magnitude of the force exerted on the car by the chain is equal to the sum of the force due to gravity and the force due to the incline. [tex]F = Fg + Fi = 5902.8 N + 5.9 N = 5908.7 N.[/tex]
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Question 10: You throw a shoe with a mass of 0.3 kg towards your archnemesis
Icky Garage and it moves horizontally to the right at 20 m/s. However, Icky is slick so
she dodges the shoe and it rebounds horizontally to the left at 30 m/s. Determine
the impulse that acts on the shoe during its collision with the wall.
The impulse that acts on the shoe during its collision with the wall is -15 kg*m/s (to the left).
Calculation steps:
The initial momentum of the shoe, p1 = mv1 = 0.3 kg * 20 m/s = 6 kgm/s (to the right)
The final momentum of the shoe, p2 = mv2 = 0.3 kg * (-30 m/s) = -9 kgm/s (to the left)
The change in momentum, Δp = p2 - p1 = -9 kgm/s - 6 kgm/s = -15 kg*m/s (to the left)
Therefore, the impulse acting on the shoe during its collision with the wall is J = Δp = -15 kg*m/s (to the left)
What is impulse?
Impulse refers to the change in momentum of an object when a force is applied to it for a certain amount of time. It is defined as the product of the force and the time for which it acts on an object. Mathematically, impulse can be expressed as:
J = F * Δt
where J is the impulse, F is the force applied, and Δt is the time for which the force acts.
What is momentum?
Momentum is a physical quantity that measures the motion of an object. It is defined as the product of an object's mass and velocity. In other words, momentum = mass x velocity.
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