After a girl delivering newspapers travels three blocks west, four blocks north, and then six blocks east, her total displacement is 5 blocks. While the total distance covered is 13 blocks.
What is displacement?A displacement is a vector in geometry and mechanics whose length is the smallest distance between the beginning and final positions of a moving point P.
If an item moves relative to a reference frame, such as a lecturer moving to the right of a whiteboard or a passenger moving toward the back of an airliner, the object's location changes. This shift in location is referred to as displacement.
Displacement (change in position) = Last position – initial position
To Calculate displacement, let displacement be (d)
d = -3i + 4j + 6i (-i because she turned west, +i because she turned east)
d = 3i + 4j
d = √(3² + 4²)
d = √(9 + 16)
d = √25
d = 5 blocks.
Total distance (Td_ = Sum of all the blocks traveled.
Td = 3 + 4 + 6
Td = 13 blocks.
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a solenoid of radius 4.10 cm has 780 turns and a length of 25.0 cm. (a) find its inductance. mh (b) find the rate at which current must change through it to produce an emf of 70.0 mv. (enter the magnitude.) a/s
(a)- The Inductance of the given coil is 6.10mH.
(b)- The rate of the current for which the coil will produce an emf of 70mV is 11.47 A/s
Solution: -
Given
Radius of the coil = 4.10cm
Number of turns of the coil = 480 Turns
Length of the coil = 25 cm
(a)
Inductance of the coil = µ * (N^2) * (A/L)
Inductance = 4π x 10^-7 * (480)^2 * π *( 0.041m)^2 /0.25m
Inductance = 1.256 x 10^-6 * (480)^2 * π *(0.041)^2 /0.25m
Inductance= 1.52* 10^-3/0.25
Inductance= 6.10mH
(b)
Δi/Δt = emf/Inductance
Δi/Δt = 70 x10^-3/6.10mH
Δi/Δt= 11.47 A/s
Therefore the inductance of the coil is denoted as 6.10mH and the rate at which the current will flow the coil to give an emf of 70mV is 11.47 A/s.
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coherent light of frequency is shone through a single slit with a gap width equal to a. an interference pattern is observed on the screen a distance behind the slit. what effect will each of the following alterations have on the width of the central bright spot on the screen? a. decrease the gap width. b. decrease the frequency of the light. c. decrease the distance from the slit to the screen.
Coherent light at this frequency passes through a single slit with an interval width equal to the effect of each of the following changes on the width of the central bright spot on the screen. reduce gap width
Two wave sources are coherent if they have the same frequency and waveform. Interference is an ideal property of waves that allows for fixed interference. The central bright band of the single slit diffraction pattern is generated by constructive interference from all secondary sources.
The width of the center band is inversely proportional to the slot width. Coherence is a fixed ratio between wave phases in a beam of radiation of one frequency. The wavelengths of two rays are coherent when the phase difference is constant. Inconsistent if there are random or changing phase relationships. When two waves are monochromatic and in phase, they are said to be coherent. A coherent source is one that generates those waves. With the help of these waves, you can study the properties of the light path. For this purpose, one beam is transmitted along the intended track, and the other is transmitted to the control test.
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OPEN ENDED QUESTION
The skater eventually comes to a stop.
What has happened to all of the skater's
original potential energy?( this is on the Ed puzzle skate park please help I’m about to cry
Answer:
The maximum amount of kinetic energy the skateboarder can have is entirely dependent on the amount of potential energy of the system.
Explanation:
As the skateboarder moves, her potential energy is converted to kinetic energy (KE), or the energy of motion as her position changes along the track and the velocity changes.
Answer:
Explanation:
Kinetic energy turned into internal energy.
Potential energy has not changed.
Efficiency of Machines Quick Check
Which is the equation for a machine's efficiency? (1 point)
O Efficiency
O Efficiency input energy - output energy
input energy . 100
=
=
=
output energy
input energy
O Efficiency output energy
O Efficiency input energy + output energy
=
. 100
The equation for a machine's efficiency is Efficiency = Output energy / Input energy * 100
Efficiency = ( Output energy / Input energy ) * 100
The efficiency of an ideal machine is 100% where Output energy is equal to Input energy. The efficiency cannot be greater than 100% in any machine. Because work done by the machine cannot be more than the work done on the machine.
The efficiency of a machine in real world is always less than 1 because some of the input energy is lost as friction or heat in any type of machine. So the ideal machine is possible in real world applications.
Therefore, the equation for a machine's efficiency is Efficiency = Output energy / Input energy * 100
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Air pressure increases as you travel higher above sea level. This is the reason that cabins in commercial airliners require pressurization.
True
False
The answer is true about the cabins in commercial airliners that require pressurization.
Why are the cabins of commercial airplanes pressurized?Airplanes are pressurized because the air is very thin at the high altitude where they fly. The passenger jet has a cruising altitude of about 30,000 - 40,000 feet. At this altitude or height, humans can't breathe very well and our body gets less amount of oxygen. Most aircraft cabins are pressurized to an altitude about 8,000 feet. This is called cabin altitude. Aircraft pilots have access to the control's mode of a cabin pressure control system and if needed it can command the cabin to depressurize.
So we can conclude that cabins in commercial airliners require pressurization because of the greater pressure of the surrounding environment.
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10. What is the solution of the equation
-9x + 4 = -8- 5x?
A x = -3
B x=
2/7
x = 1
℗ x = 3
Answer:
x=3
-9x+4= -8-5x
+5x +5x
-4x+4= -8
-4 -4
-4x= -12
/-4. /-4
x=3
a 6.0-kg fish swimming 1.1 m/s swallows an absentminded 1.0-kg fish swimming toward it at a speed that brings both fish to a halt immediately after lunch. find the speed of the approaching smaller fish before lunch.
The speed of the approaching smaller fish before lunch is 6m/s.
What is the speed?The entire distance that an object travels in a predetermined amount of time is the definition of speed.
Given that the speed v₁ of big fish is 1 m/s and mass m₁ is 6kg. The mass m₂ of small fish is 1 kg.
Both fish have linear momentum of,
p₁ = m₁v₁ + m₂v₂
Where,
p₁ is the initial linear momentum
v₂ is the speed of the small fish.
Since both fish are traveling in the same direction and v is their ultimate meeting velocity, the final linear momentum will be given as,
p₂ = (m₁ + m₂) v
Linear momentum is held constant hence,
p₁ = p₂
m₁v₁ + m₂v₂ = (m₁ + m₂) v
The fish's final speed will be zero because they stopped moving., so
m₁v₁ + m₂v₂ = 0
v₂ = - m₁v₁/m₂
v₂ = -6×1/1
v₂ = -6
The negative symbol indicates that the tiny fish are swimming against the current.
The speed of the approaching smaller fish before lunch is 6m/s.
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during keon's golf drive, the angular velocity of his club is zero at the top of the backswing and 33 rad/s at the bottom of the downswing just before ball impact. the downswing lasts 0.29 s, and the distance from the club head to the axis of rotation is 1.88 m at the bottom of the downswing. what is the average tangential acceleration of the club during the downswing (in m/s2)?
The average tangential acceleration of the club during the downswing is 113.79 rad/s².
Centripetal acceleration is due to the change within the direction of tangential speed, whereas tangential acceleration is due to any trade inside the value of the tangential speed.
The tangential acceleration is while the rotational velocity adjustments, that is 0 for uniform circular motion. while vector speed adjustments path however not important. for this reason Tangential acceleration =zero. Angular acceleration is the trade in angular velocity divided by using time, whilst tangential acceleration is the change in linear speed divided through time.
given,
∆ ω = 33 rad/s
∆t = 0.29 sec
α = (change in ω)/(change in t)
α = 33 rad/s / 0.29 s = 113.79 rad/s²
tangential acceleration = r α = 1.88*113.79 = 213.93 m/s2
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If the same elevator accelerates downwards
with an acceleration of 1.2 m/s
2
, what is the
upward force exerted by the elevator floor on
the passenger?
The upward force exerted by the elevator floor on the passenger is 7.6 times mass of the passenger.
What is force?A force in physics is an effect that has the power to alter an object's motion. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Given in question elevator accelerates downwards with an acceleration of 1.2 m/s². There is acceleration due to gravity working downward which is 9.8 m/s².
So, net acceleration due to gravity is given as 9.8 - 1.2 = 7.6 m/s²
The upward force exerted by the elevator floor on the passenger is mass times acceleration, 7.6 times mass of passenger.
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b. A bus travelling in a straight seconds. road covers a distance of 220m in 20 between mass and weight. calculate its velocity
Answer:
11 m/s?
Explanation:
The question is not clear, but I am assuming that it is asking for the velocity of a bus traveling for 220 meters in 20 seconds.
You are Given:
Displacement (d) : 220m (in this question, since there is no change in direction, the distance and displacement is the same)
Time (t) : 20 seconds
You want to Find:
Velocity: ???
Equation to use:
velocity = displacement/time
aka. v = d/t
Now just Solve:
v = d/t
v = 220m/20s
v = 11 m/s
1. A vector of 15 units acts to the left, and a vector of 3 units acts to the right. What is the resultant?
Answer: 12
Explanation:
The resultant vector is 12 unit.
What is addition of two vector?When two vectors point in the same direction, their sum is equal to the total of their respective magnitudes pointing in the same direction.
When two vectors are pointed in opposite directions, the resultant vector is pointed in the direction of the larger vector and is equal to the difference between their magnitudes.
Here, one vector of 15 unit is acting to the left and another vector of 3 unit acting rightwards. As they are acting in opposite direction, vector summation of two vector will be equal to the value of subs traction of their magnitude.
So, Resultant vector= 15 unit + (-3 unit)
= 15 unit - 3 unit
= 12 unit.
Hence, the resultant vector will be 12 unit.
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what is the momentum of an 7.2- kg bowling ball rolling at 3.0 m/sm/s ? express your answer to two significant figures and include the appropriate units.
The momentum of an 7.2 kg bowling ball rolling at 3 m/s is 21.6 kgm/s.
What is momentum and how the momentum of bowling ball calculated out to be 21.6 kgms?Momentum is defined simply as the quantity of motion of the body , but it is the product of mass and velocity.There are several kind of momentum like linear momentum, translational momentum.Here is given the mass of the object 7.2 kg and the velocity is 3 m/s of the ball.Now to calculate the momentum we will simply apply the formula momentum = mass x velocity.7.2 x 3 = 21.6 kg-m/s is the momentum of the bowling ball rolling at 3 m/s .To know more about momentum visit:
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Forces with magnitudes of v = 135 newtons and u = 280 newtons act on a hook (see figure). The angle between the two forces is 45°. Find the direction and magnitude of the resultant of these forces. (Hint: Write the vector representing each force in component form, then add the vectors. Round your answers to two decimal places.)
To find the resultant force we will first find the component force of the forces given, to do this, we need to remember that any vector can be express in component form by:
[tex]\begin{gathered} \vec{v}= \\ \text{ where } \\ v\text{ is the magnitude } \\ \theta\text{ is the angle of the vector with respect to the positive x-axis.} \end{gathered}[/tex]For force u we notice that its magnitude is 280 N and its angle is zero, then we have:
[tex]\begin{gathered} \vec{u}=<280\cos0,280\sin0> \\ \vec{u}=<280,0> \end{gathered}[/tex]For force v we know that its magnitude is 135 N and its angle is 45°, then we have:
[tex]\begin{gathered} \vec{v}=<135\cos45,135\sin45> \\ \vec{v}=<95.46,95.46> \end{gathered}[/tex]Now that we have both vectors in component form we add them to get the resultant in component form:
[tex]\begin{gathered} \vec{F}=\vec{u}+\vec{v} \\ \vec{F}=<280,0>+<95.46,95.46> \\ \vec{F}=<375.46,95.46> \end{gathered}[/tex]Once we have the resultant force in component form we can find its magnitude and direction if we remember that they are given by:
[tex]\begin{gathered} F=\sqrt{F_x+F_y} \\ \theta=\tan^{-1}(\frac{F_y}{F_x}) \end{gathered}[/tex]Plugging the values we found for the components we have:
[tex]\begin{gathered} F=\sqrt{375.46^2+95.46^2} \\ F=387.41 \end{gathered}[/tex]and
[tex]\begin{gathered} \theta=\tan^{-1}(\frac{95.46}{375.46}) \\ \theta=14.27 \end{gathered}[/tex]Therefore, the magnitude of the resultant force is 387.41 N and the direction is 14.27°
suppose a 62-turn coil lies in the plane of the page in a uniform magnetic field that is directed into the page. the coil originally has an area of 0.25 m2. it is stretched to have no area in 0.100 s. what is the magnitude of the induced emf (in volts) if the uniform magnetic field has a strength of 1.50 t?
The magnitude of electromotive force is 232.5 volts.
We need to know about the electromotive force of induction to solve this problem. The emf induction appears when there is any change in magnetic flux. The magnitude of emf can be determined by
ε = N dΦ / dt
where N is coil turns, ε is electromotive force, dΦ is change in magnetic flux and dt is time interval.
From the question above, the parameters given are
N = 62
A/t = 0.25 m² / 0.1 s
t = 0.1 s
B = 1.5 T
By substituting the given parameters, we can calculate electromotive force
ε = N . dΦ / dt
ε = 62 . B . A / t
ε = 62 . 1.5 . 0.25 / 0.1
ε = 232.5 volts
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a marble is rolling across a flat surface with a velocity of 2 m/s. it begins to roll up a ramp. ignoring rotational kinetic energy and friction, what will be the vertical height of the marble when it comes to a stop before rolling back down?
The vertical height of the marble when it comes to a stop before rolling back is 20 centimeters.
As per the Law of conservation of energy,
If there is no external force acting on the system, the energy will always remains the same at every point of the motion.
As, we can see, there is no external force on the marble,
Energy of the marble at start will be equal to energy of the marble at the vertical height
We can write,
Energy while rolling = Energy at the highest point
1/2MV² = MgH
Where,
M is the mass of the marble,
V is the velocity of the marble,
g is the acceleration due to gravity and,
H is vertical height of the marble.
So,
1/2MV² = MgH
1/2V² = gh
Putting all the values,
1/2(2)² = 10H
H = 4/20
H = 0.2 meters.
So, the vertical height of the marble is 20 cm.
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What is your total displacement if you walk 30m East and 50m North?
The total displacement would be 110m.
The total distance is 50 m + 30 m + 30 m = 110 m. The displacement is the shortest route from the starting point. It is solved using vectors.
What is Displacement?
Displacement is a vector quantity which depends on the direction of motion but distance is a scalar quantity which just sums up all the given quantity values. The displacement is simply the difference between the locations of the two markers and is unrelated to the route used to get there. It is a vector quantity that has a direction and magnitude.
Hence, the total displacement if you walk 30m East and 50m North would be 110m.
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Answer:
58.31 meters northeast
Explanation:
The displacement can be modeled into the vector equation of [tex]\displaystyle{\vec s = 30\hat x + 50\hat y}[/tex]. We can find the magnitude of displacement by applying Pythagoras Theorem. Suppose we have a two-dimensional vector equation [tex]\displaystyle{\vec v = a\hat x + b\hat y}[/tex] then the magnitude of vector is [tex]\displaystyle{|\vec v\, | = \sqrt{a^2+b^2}}[/tex].
Therefore, the magnitude of displacement is:
[tex]\displaystyle{|\vec s\, | = \sqrt{30^2+50^2}}\\\\\displaystyle{=\sqrt{900+2500}}\\\\\displaystyle{=\sqrt{3400}}\\\\\displaystyle{\approx 58.31 \ \sf m}[/tex]
Since 30 meters east and 50 meters north form northeast direction then the displacement is 58.31 meters northeast.
What is the weight of a boy with a mass of 50 kg on Earth?
Use g= 9.81 m/s² and do not include units in your answer.
Answer:
490.5
Explanation:
Force = Mass × Acceleration
Since, Weight is a force and 'g' is the acceleration due to the earth's gravity,
Weight = Mass × g
Weight = 50 kg × 9.81 m/s² = 490.5 kg-m/s² or 490.5 N
As shown in the diagram below, a soccer player kicks a ball directly toward the goal along a displacement vector r, which has a length of 7.7 m and a direction 30 degrees east of south. Alternatively, she could have kicked it to a second player standing directly in front of the goal along a displacement ry, who could have then kicked it to the goal along a displacement vector rx, as shown. Find the magnitudes (in m) and directions of rx and ry
Given that, the soccer player makes a displacement r = 7.7 m from the goal.
The distance between this player and the second player is [tex]r_{y}[/tex], and the distance between the second player and the goal is [tex]r_{x}[/tex]. The angle made by the first player with the goal is θ = [tex]30^{0}[/tex] east of south.
The magnitudes of [tex]r_{x}[/tex] and [tex]r_{y}[/tex] can be determined using the trigonometric rules.
r is the hypotenuse of the triangle formed (as shown in figure in the question), and [tex]r_{x}[/tex] is the side of triangle which is opposite to the angle θ = [tex]30^{0}[/tex]. So, [tex]r_{x}[/tex] = r sinθ = 7.7m × sin(30°) = 3.85 m.
[tex]r_{y}[/tex] is the side of triangle adjacent to the angle θ = [tex]30^{0}[/tex]. So, [tex]r_{y}[/tex] = r cosθ = 7.7m × cos(30°) = 5.445 m.
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Describe and explain a danger to a driver of not wearing a safety belt during a sudden stop.
a thin rod of length 3.15 m and mass 12.7 kg is rotated at an angular speed of 3.60 rad/s around an axis perpendicular to the rod and through one of its ends. find the magnitude of the rod's angular momentum.
The magnitude of the rod's angular momentum is 165.92 [tex]Kg m^{2} s^{-1}[/tex].
The moment of inertia for the rod through an axis 'perpendicular' to one of its ends is given by :
[tex]I=\frac{Ml^{2} }{3}[/tex] (where M = mass of rod , l = length of rod)
Now, the angular momentum of the rod is given by;
L= Iω
= [tex]\frac{Ml^{2} }{3}[/tex]×ω
=[tex]\frac{12.7Kg * (3.15 m^{2})}{3}[/tex]* [tex]3.95 rad s^{-1}[/tex]
= 165.92 [tex]Kg m^{2} s^{-1}[/tex]
∴ The required angular momentum is: 165.92 [tex]Kg m^{2} s^{-1}[/tex]
As the rotating equivalent of linear momentum in physics, angular momentum (rarely a moment of momentum or rotational momentum) is used. It is a conserved quantity, meaning that in a closed system, the total angular momentum stays constant, making it a significant physical quantity. The magnitude and direction of angular momentum are both conserved. The conservation of angular momentum is responsible for the useful characteristics of bicycles, motorcycles, frisbee-lead bullets, and gyroscopes. Hurricanes develop spiral structures and neutron stars rotate rapidly due to the conservation of angular momentum. Conservation generally sets a limit on a system's potential motion but does not determine it in any way.
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If you are 16 miles from Charleston, how long will it take to get there if your average velocity is 42
miles per hour?
Answer:
22.9 minutes
Explanation:
Distance = Speed x Time
We want the time to go 16 miles at 42 miles/hour (mph).
16 miles = (42 mph)*T
T = 16 miles/(42 miles/hr)
Time = 0.381 hours
(60 minutes/hour)*(.381 hours)= 22.9 minutes
In a 92 s interval, 562 hailstones strike a glasswindow of area 1.216 m² at an angle 64° to thewindow surface. Each hailstone has a mass of2 g and speed of 5.8 m/s.If the collisions are elastic, find the averageforce on the window.Answer in units of N.
Given that the number of hailstones is n = 562
The mass of hailstone is m = 2 g = 0.002 kg
The speed of hailstone is v = 5.8 m/s
The time taken will be t = 92 s
The angle is
[tex]\theta=64^{\circ}[/tex]We have to calculate the force.
The force can be calculated by the formula
[tex]\begin{gathered} F=\text{ force due to one hailstone }\times numberofhailstones\text{ } \\ =m\frac{v}{t}\sin \theta\times n \end{gathered}[/tex]Substituting the values, the force will be
[tex]\begin{gathered} F=\text{ }\frac{\text{0.002}\times5.8\times\sin 64^{\circ}\times562}{92} \\ =0.063\text{ N} \end{gathered}[/tex]if a 3.0 kg toy is moving at 4.0 m/s then what would be kentic energy of the cart is moving twice as faster
It tells us that a toy has a mass of 3.0 kg, with a speed of 4.0 m/s.
We apply the following formula:
Ec = m * v²/2
We replace data and solve:
Ec = 3.0 kg* (4.0 m/s)²
Ec = 3.0 kg* 16 m²/s²/2
Ec = 48 kg * m²/s²/2
Ec = 24 kg * m²/s²
Ec = 24 N * m ========> Joules units
Ec = 24 J
The new cartia of the cart would be of 24 joules.in which reference frame is the translational (nonconvertible) kinetic energy greater: the reference frame in which the bat is at rest immediately before the collision or the reference frame in which the ball is at rest immediately before the collision?
The reference frame in which the bat is at rest immediately before the collision is the reference frame in which translational (nonconvertible) kinetic energy is greater.
As translational (nonconvertible) kinetic energy is greater when the bat is at rest because when it will be at rest the mass will be more. The translational dynamic energy of a body is rise to one-half the item of its mass and the square of its speed.
The translational kinetic energy depends on movement through space, and for an inflexible body of consistent mass, it rises to the item of half the mass times the square of the speed.
The movement of an unreservedly falling body could be a translational active vitality. Kinetic rangy at a pivoting fan is rotational kinetic energy.
In material science, the dynamic energy of a protest is the vitality that it has due to its movement. It is characterized as the work required to quicken a body of a given mass from rest to its expressed speed.
Having picked up this vitality amid its speeding up, the body keeps up this motor vitality unless its speed changes. The same sum of work is done by the body when decelerating from its current speed to a state of rest.
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an engine flywheel initially rotates counterclockwise at 6.75 rotations/s. then, during 23.1 s, its rotation rate changes to 2.97 rotations/s clockwise. find the flywheel's average angular acceleration (including its sign) in radians per second squared. define counterclockwise rotation as positive
Flywheel's average angular acceleration is +0.42 radian per second square.
Angular acceleration is the rate of change of angular velocity and is denoted by "a".
Rate at which an object revolves or rotates about an axis is known as angular velocity and is denoted by "w".
Initial Angular velocity is denoted as w1 and final angular velocity is denoted as w2.
So, according to the equation of rotational motion,
w2= w1+at
Where t is the time
When we put the values given in this equation
= +2.97= -6.75+ a×23.1
= +2.97+6.75=a×23.1
= 9.72= 23.1×a
So, a= +0.42
Rate of change of angular velocity of flywheel is +0.42.
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6. A ball rolls off a table and falls 0.75 m to the floor, landing with a speed of 4.0 m/s. 1. What is the acceleration of the ball just before it strikes the ground? 2. What was the initial speed of the ball? 3. What initial speed must the ball have if it is to land with a speed of 5.0 m/s?
1 ) Acceleration of the ball just before it strikes the ground = 10.67 m/s²
2 ) The initial speed of the ball = 1.15 m / s
3 ) The initial speed of the ball if the ball lands at 5.0 m/s = 3.2 m / s
v² = u² + 2 a s
v = Final velocity
u = Initial velocity
a = Acceleration
s = Displacement
1 ) In vertical motion,
v = 4 m / s
s = 0.75 m
u = 0
4² = 0 + ( 2 * a * 0.75 )
a = 16 / 1.5
a = 10.67 m / s²
2 ) The initial speed of the ball,
Resolving the velocity into its horizontal and vertical components,
[tex]V_{y}[/tex]² = [tex]U_{y}[/tex]² + 2 a s
[tex]V_{y}[/tex]² = 0 + ( 2 * 9.8 * 0.75 )
[tex]V_{y}[/tex] = 3.83 m / s²
V² = [tex]V_{x}[/tex]² + [tex]V_{y}[/tex]²
4² = [tex]V_{x}[/tex]² + 3.83²
[tex]V_{x}[/tex] = √ 16 - 14.67
[tex]V_{x}[/tex] = 1.15 m / s
[tex]V_{x}[/tex] = [tex]U_{x}[/tex] = 1.15 m / s
3 ) If the ball lands with a speed of 5.0 m/s,
V² = [tex]V_{x}[/tex]² + [tex]V_{y}[/tex]²
5² = [tex]V_{x}[/tex]² + 3.83²
[tex]V_{x}[/tex] = √ 25 - 14.67
[tex]V_{x}[/tex] = 3.2 m / s
[tex]V_{x}[/tex] = [tex]U_{x}[/tex] = 3.2 m / s
Therefore,
1 ) Acceleration of the ball just before it strikes the ground = 10.67 m/s²
2 ) The initial speed of the ball = 1.15 m / s
3 ) The initial speed of the ball if the ball lands at 5.0 m/s = 3.2 m / s
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The main engine of an ariane v rocket produces a thrust of 1015 kN and it’s booster rockets produce a total thrust of 13300 kN. If it has a launch mass of 780 tonnes, calculate its initial acceleration.
The initial acceleration of the rocket at the given thrust is 1.3 m/s².
What is the initial acceleration of the rocket?
The initial acceleration of the rocket is determined by Newton's second law of motion. This law states that the force applied to an object is directly proportional to the product of mass and acceleration of the object.
F = ma
where;
F is the applied forcem is the mass of the rocketa is the accelerationThe initial lunch force = 1015 kN = 1,015,000 N
The mass of the rocket = 780 tonnes = 780,000 kg
a = F/m
a = (1,015,000) / (780,000)
a = 1.3 m/s²
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f a stone is thrown vertically upward from the surface of the moon with a velocity of 10 m/s, its height (in meters) after seconds is . (a) what is the velocity of the stone after 7 seconds? (b) what is the velocity of the stone after it has risen 25 m?
a) The velocity of stone after 7 seconds is 1.62 m/sec.
b) The velocity of the stone after it has risen 25 m is -[tex]\sqrt{17}[/tex]
a) h(t) = 10t - 0.83[tex]t^{2}[/tex]
velocity = [tex]\frac{dh}{dt}[/tex](t) = 10 - 2*0.83*t
[tex]\frac{dh}{dt}[/tex] (7) = 10 - 2*0.83*7
= 1.62 m/sec
The stone after 7 seconds is 1.62 m/sec
b) h(t) = 25
10t - 0.83[tex]t^{2}[/tex] = 25
t = 50/83 (10 + [tex]\sqrt{17}[/tex])
[tex]\frac{dh}{dt}[/tex] = 10 - 2*0.83*(50/83)(10 + [tex]\sqrt{17}[/tex])
= 10 - (10 + [tex]\sqrt{17}[/tex])
= - [tex]\sqrt{17}[/tex] m/sec.
The stone after it has risen 25 m is - [tex]\sqrt{17}[/tex] m/sec.
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A student is pulling a wagon and records the force vs time values in the table, which of the following will also remain constant for the wagon
A student is pulling a wagon and records the force vs time values in the table, then the acceleration of the wagon would remain constant, therefore the correct answer is option D.
What is Newton's second law?
Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum.
As given in the problem if a student is pulling a wagon and records the force vs time values in the table,
As the Force of the pulling is constant and assuming the mass of the wagon to be constant the acceleration of the wagon would not change.
Thus, the correct answer is option D.
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The question is incomplete, the complete question is,
A student is pulling a wagon and records the force vs time values in the table, which of the following will also remain constant for the wagon
A. Displacement
B. velocity
C. Momentum
D. Acceleration
Galileo’s pendulum theory stated that the time taken to swing through one complete cycle of a pendulum depends on what?
Italian astronomer, physicist, and engineer Galileo di Vincenzo Bonaiuti de' Galilei was sometimes referred to be a polymath.
Galileo asserted that the length of a pendulum affects how long it takes to swing through a full cycle.
A weight suspended from a pivot such that it can freely swing is called a pendulum. Gravity exerts a restoring force on a pendulum that causes it to accelerate back toward its equilibrium position when it is sideways from its resting position.
A pendulum is a tool for tracking periodic motion. It is made out of a string that is fastened to a sturdy structure. Typically, a pendulum swings from side to side when it is shifted through a tiny angle.
The length of the pendulum determines how long it takes for it to swing through one full cycle. The "period of the pendulum" is when things happen.
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