Two protons and two neutrons are both present in the particle that an unstable nucleus releases.
What does alpha decay mean?The nuclear process known as "alpha decay" results in the parent nucleus emitting an alpha particle. The alpha particle, represented by the Greek letter and physically similar to the helium atom's nucleus, is made up of two protons and two neutrons.
Which statement about alpha decay is accurate?What statement about deterioration is true? It brings down the atomic number of the nuclide by 2. The daughter nuclide, which frequently doesn't undergo further decay since the parent nuclide is unstable, is created during radioactive decay.
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An elevator in a hotel starts at ground level. It rapidly moves up to the third floor, where it stops to unload passengers. The elevator then descends to the basement at a slower speed than before.
Identify whether or not the graph correctly represents the story. Explain your answer in 1-2 sentences.
The graph does not correctly represent the story because the elevator descends to the basement at a faster speed than before.
What is the upward motion of an elevator?
An elevator going up shows uniform linear motion, as elevator will move in a straight line with a constant speed.
This type of motion can be shown using a straight line graph.
The downward motion of an elevator descending or moving downwards can be explained as follows;
An elevator moving downwards shows uniform linear motion, as elevator will move in a straight line with a constant speed.
From the given graph we can conclude the following;
During the upward motion of the elevator, at point A, the elevator moved up gradually.At point B the elevator maintained a constant speedduring the downward motion at point C, the moved down more quickly than during the upward motion.Thus, from the greater steepness of the downward motion of the elevator than the upward motion, we can conclude that the elevator descends to the basement at a faster speed than before.
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Figure 5 shows a ray of light in an optical fibre.
Figure 5
Inside of optical fibre
What is the name given to the dotted line on Figure 5?
[1 mark]
The technology that sends information as light pulses via a glass or plastic fiber is known as fiber optics, or optical fiber. These glass fibers can range in quantity from a few to several hundred in a fiber optic cable. The glass fiber core is encircled by yet another glass layer known as cladding.
What fiber optics does and how it works?In fiber optics, data is sent as pulses of light, or photons, that travel over a fiber optic cable. Incoming light is bent at a specific angle due to the differing refractive indices of the glass fiber core and cladding.
Total internal reflection is the method by which light signals traveling through fiber optic cable bounce off the core and cladding in a series of zigzag motions. Due to the thick glass layers, the light signals move around 30% slower than the speed of light instead of at the speed of light.
Fiber optic transmission sometimes needs repeaters at a distance to renew, or amplify, the signal throughout its path. By converting the optical signal to an electrical signal, processing that electrical signal, and then retransmitting the optical signal, these repeaters regenerate the optical signal.
Up to 10 Gbps transmissions can currently be supported by fiber optic connections. A fiber optic cable often gets more expensive as its bandwidth capacity increases.
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When inflating a balloon, which of the following represents an equal but opposite force acting on the balloon?
A.) releasing the balloon
B) the air entering the balloon
C) tying the balloon
D) the expansion of the balloon
When inflating a balloon, the expansion of the balloon represents an equal but opposite force acting on the balloon; option D.
What are equal and opposite forces?Forces are agents which cause a change in the motion of an object moving in a straight line or an object at rest to change its position.
According to the third law of motion, reaction and action are equal and opposite forces.
This law is seen in the inflation of balloons.
When a balloon is being inflated, the force applied in inflating the balloon pushes against the wall of the balloon. The balloon acts in an equal opposite direction by forcing the air molecules together, thus increasing the pressure of the air inside the balloon.
Therefore, an equal and opposite force is exerted by the air molecules o the air molecules.
When the balloon is released, the air is forcefully forced out in the opposite direction.
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Answer:
its D
Explanation:
the person above is correct too
two people push a 2,159. kg car to get it started. an acceleration of at least 3.4 m/s2 is required to start the car. assuming both people apply the same magnitude force in the same horizontal direction, how much force will each need to apply if friction between the car and the road is 310 n? express your answer in scientific notation. n
The force needed to be applied by each person is 5.150×10^3 N.
The required acceleration is 3.4 m/s2 and the mass of the car is 2,159 kg.
According to Newton's second law:
F = ma
F = 2,159 × 3.4.
F = 7340.6 N
Adding the force of friction into it
F = 7340 + 310
F = 7650.6 N
Since two people need to apply the force
F = 7650 N / 2
F = 3,825.3 N
or
F = 3.825×10^3 N
The force applied by each person to push the car is 3.825×10^3 N.
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Pick the answer that correctly completes the sentence: as a sound wave approaches an observer the frequency will _____, the wavelength will____, and the speed of sound will______.A) decrease; increase; stay the same B) increase; increase; increase C) increase; decrease; stay the same D) decrease; decrease; increase
To find
Pick the answer correctly that fits the sentence.
Explanation
In a doppler effect, when a sound source apporaches a observer, its frequency increases. As wavelength is inversely proportional so the wavelength decreases. Speed of sound ina given medium is constant, so the speed of sound doesnot change
Thus,
as a sound wave approaches an observer the frequency will increase, the wavelength will decrease, and the speed of sound will stay the same.
Conclusion
The correct option is C) increase; decrease; stay the same.
what is the speed of the block when it has moved a distance of 0.0150 m from its initial position? (at this point the spring is compressed 0.0220 m .)
The speed of the block when it has moved a distance of 0.0150 m from it's initial position is 0.32 m/s .
When a spring is compressed by a force F, the potential energy is stored on it.
If the spring is released, the potential energy turns into kinetic energy.
The object is replaced by the call-back force which occurs on the spring F' = K.∆x
K= 815 N/m
∆x= 0.0190 m
F' = 815.0.019 = 15.8 N
Ff= k.m.g
Ff = 0.35 . 2.55. 9.81 = 8.76 N friction force acceleration of object is-
a= F' - Ff/m
V^2 = 2.a . displacement
V^2 = 2.264. 0.0200.
V^2 = 0.1056
V=√0.1056.
V= 0.32 m/s
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suppose you observe a small star orbiting a much larger star. you observe that the small star is orbiting at a distance of 20 au (in terms of the semi-major axis of its orbit), and with an orbital period of 2 years. how massive is the large star? (hint: for this problem you can assume that the small star has a much smaller mass than the large star.)
The mass of the large star based on orbital period is 6912 x 10³⁰ kg.
We need to know about the orbital period to solve this problem. The orbital period depends on the semi-major axis, gravitational constant, and the mass of the massive object. It can be written as
T² = 4π².a³ / GM
where T is the orbital period, a is the semi-major axis, G is the gravitational constant and M is the mass.
From the question above, the given parameters are
a = 24 au = 24 . ³√(G.Msun yr²/ 4π²)
T = 2 years
Msun = 2 x 10³⁰ kg
By substituting the given parameters, we get
T² = 4π².a³ / GM
2² = 4π². (24 . ³√(G.Msun yr²/ 4π²))³ / GM
4 = 13824 Msun / M
M = 6912 x 10³⁰ kg
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n sussex county, delaware, a post-halloween tradition is punkin chunkin, a competition in which contestants build cannons, catapults, trebuchets, and other devices to launch pumpkins to the greatest distance they can. tough hard to believe, pumpkins have been projected a distance of 1245 m (over 3 4 mi) in this contest. what is the minimum initial speed needed for such a shot?
110.53m/s is the minimum initial speed or initial velocity needed for such a shot.
The lowest speed at which a particular range is attained is determined. It is stated the distance that the pumpkins were hurled. By inserting the range of the pumpkin and the acceleration owing to gravity, the minimal velocity at which they were launched to go this distance was determined.
[tex]R=u_m^2/g[/tex]
[tex]1245.41m=(u_m^2/9.80m/s^2[/tex]
[tex]u_m^2=12217.47[/tex]
[tex]u_m=110.53m/s[/tex]
Any object susceptible to forces will move more quickly. This acceleration causes a change in the object's velocity. The speed of the item prior to the change brought on by acceleration is therefore known as the initial velocity. The speed will be the final speed once the object has been accelerating for some time.
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A concave mirror has a focal length of 0.50 m. If an object produces a virtual image 0.19 m from the mirror, where is it located?
In order to calculate the object's position, we can use the formula below:
[tex]\frac{1}{f}+\frac{1}{d_o}+\frac{1}{d_i}[/tex]Where f is the focal length, do is the object's position and di is the image's position.
Using f = 0.5 m and di = -0.19 m (we use a negative value because the image is virtual), we have:
[tex]\begin{gathered} \frac{1}{0.5}=\frac{1}{d_o}+\frac{1}{-0.19}\\ \\ 2=\frac{1}{d_o}-5.263\\ \\ \frac{1}{d_o}=2+5.263\\ \\ \frac{1}{d_o}=7.263\\ \\ d_o=\frac{1}{7.263}\\ \\ d_o=0.14\text{ m} \end{gathered}[/tex]Therefore the object is at 0.14 meters from the mirror.
its hard it have time help
Answer:
i think it's a
Explanation:
a satellite moves in a circular earth orbit that has a radius of 8.75 x 106 m. a model airplane is flying on a 20.3-m guideline in a horizontal circle. the guideline is nearly parallel to the ground. find the speed of the plane such that the plane and the satellite have the same centripetal acceleration.
The speed of the plane is 32.519 m/s
Given radius of satellite orbit is [tex]r_{1} = 8.75[/tex] × [tex]10^{6} m[/tex]
Also, Orbital velocity is given by
[tex]v = \sqrt{\frac{GM}{r} }[/tex]
where M is the mass of the earth which is equal to [tex]5.98[/tex] × [tex]10^{24}[/tex] kg
G = [tex]6.67[/tex] × [tex]10^{-11}[/tex]
[tex]v = \sqrt{\frac{(6.67 * 10^{-11} )(5.98*10^{24}) }{8.75 * 10^{6} } }[/tex]
[tex]v=21.35[/tex] × [tex]10^{3}[/tex] m/s
Centripetal acceleration is given as
[tex]a_{c} = \frac{v^{2} }{r}[/tex]
[tex]a_{c} = \frac{(21.35 * 10^{3} )^{2} }{8.75 * 10^{6} }[/tex]
[tex]a_{c} = 52.094 m/s^{2}[/tex]
For model airplane
[tex]a_{c} = \frac{v^{2} }{r}[/tex]
[tex]52.094 = \frac{v^{2} }{20.3}[/tex]
v = 32.519 m/s
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what is the magnitude n of the normal force on the block of mass m? (b) (5 points) what direction does the hanging block m move, up or down? circle one. (c) (18 points) what is the common magnitude a of the acceleration of the blocks? (d) (14 points) what is the magnitude t of the tension in the string? (e) (6 points) what is the speed of the hanging mass after a time period of 2.0 seconds?
a) The normal force on the block of mass M is 76.383 N in magnitude.
b) The hanging block goes upward in one direction.
c) The block's acceleration has a common magnitude of 8.11 m/s2.
d) The string's tension measurement is 161.19 N in magnitude.
e) After 2.0 seconds, the speed of the hanging mass is 5.695 seconds.
Simply put, "distance or quantity" is the definition of size. In terms of motion, it shows the absolute or relative size, direction, or movement of an object. It is used to describe something's size or scope. Magnitude in physics typically refers to size or quantity.
It's given that:
M = 45.2 kg.
µk = 0.10.
m = 9.0 kg.
angle = 30 degree
A) The block's mass M and the normal force's strength N:
N - mgcosθ = 0
= 9 * 9.8cos 30
= 76.383N
B) The hanging block's direction shifts upward.
C) the typical magnitude of the acceleration of the block is
Mg - T = Ma
(Mg - T) / M = a
(45.2 * 9.8 - 76.383) / 45.2 = a
[tex]8.11\frac{m}{s^{2} } = a[/tex]
D) the string's tension, T, in terms of magnitude
T - mg = ma
T = ma + mg
T = 9 * 8.11 + 9 * 9.81
T = 161.19N
E) the dangling mass's speed after a delay of 2.0 seconds
v² - u² = 2as
v² - 0² = 2as
v² = 2as
v = √2as
v = √2*8.11*2
v = 5.695 m/s
COMPLETE QUESTION: Two blocks are connected by a light but sturdy string wrapped around a mass-less pulley. The rough inclined surface makes an angle of 30 degrees with the horizontal. The block on the inclined surface has a mass M = 45.2 kg. Assume the coefficient of kinetic friction between the union of mass M and the inclined plane is µk = 0.10. The vertically hanging block has mass m = 9.0 kg. Assume the blocks begin their motion from rest.
(a) (10 points) What is the magnitude N of the normal force on the block of mass M?
(b) (5 points) In What direction does the hanging block m move, up or down? Circle one.
(c) (18 points) What is the common magnitude of the acceleration of the blocks?
(d) (14 points) What is the magnitude T of the tension in the string?
(e) (6 points) What is the speed of the hanging mass after a time period of 2.0 seconds?
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A girl on a bridge throws a rock
straight down at -12.5 m/s. It hits
the ground 38.4 m below.
How much time did it take?
(Unit = s)
answer is: 1.80 as time
Vf = -30.1
The time that is taken for the rock to land on the ground from the given height is 1.8 seconds.
What is the time taken?We know that we can be able to obtain the time that have been taken from the equations of kinematics. In this case, we have to consider the equations of kinematics which have occurred under gravity.
Let us recall that we have the fact the equation that ought to be used here is;
h = ut + 1/2gt^2
u = initial velocity
h = the height attained
t = time taken
g = acceleration due to gravity
We know that in this case, we have to use the equations of the kinematics that we can apply to the rock that is moving under the influence of gravity as to obtain the tome that it would take the rock to be able to land on the ground from the height that we have been given in the question.
Having listed out these parameters;
38.4 = -12.5t + (0.5 * 9.8 * t^2)
38.4 = -12.5t + 4.9t^2
Hence;
4.9t^2 - 12.5t + 38.4 = 0
t = 1.80 s
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Explain some endless capabilities of our vast universe?
ANSWER:
STEP-BY-STEP EXPLANATION:
Answer:
It is impossible to answer that as we could discover more than we know now in years to come with advanced technologies
Explanation:
Johnny is driving North at 42 mph. Then drives west at 37 mph. What is the resultant velocity?
A) 55.9 mph North
B) 5 mph West
C) 55.9 mph Northwest
D) 79 mph Northwest
If Johnny is driving North at 42 miles per hour and drives west at 37 miles per hour, then the resultant velocity would be 55.9 mph north, therefore the correct answer is option A.
What is Velocity?The total displacement covered by any object per unit of time is known as velocity. It depends on the magnitude as well as the direction of the moving object.
As given in the problem Johnny is driving North at 42 mph. Then drives west at 37 mph.
The resultant velocity of the Jhonny = √ ( 42² + 37² )
= 55.97 miles per hour
Thus, the resultant velocity of Jhonny would be 55.9 mph north, therefore the correct answer is option A.
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An engineer is troubleshooting trying to figure out the value of a capacitor. She knows that the charge value is 480 coulombs and the power supply feeds 110 V. What's the capacitor value?Question 19 options:A) 128B) 4.36C) 0.88D) 5,400
We can use the formula of the capacitance
[tex]C=\frac{Q}{V}[/tex]where C is the capacitance, Q is the charge and V is the voltage.
In our case
Q=480 C
V= 110 V
[tex]C=\frac{480}{110}=4.36\text{ F}[/tex]The value of the capacitor is 4.36 F
ANSWER B) 4.36F
A cosmic-ray electron moves at 7. 5 × 10^6 m/s perpendicular to earth’s magnetic field at an altitude where the field strength is 1. 0 × 10^-5t. What is the radius of the circular path the electron follows?.
4.266 m is the radius of the circular path the electron follows
Electron's speed = 7.50 × 10⁶ m/s
Magnetic field, B = 1 × 10⁻⁵ T
Electron's mass. m = 9.11 × 10⁻³¹
Charge of electron, q = 1.6 × 10⁻¹⁹
We know the relation of radius of curvature, = 4.266 m
What is a circle's radius of curvature?Every point on a circle has a curvature that is equal to the reciprocal of the radius; for other curves (and straight lines, which can be thought of as circles of infinite radius), the curvature is equal to the reciprocal of the radius of the circle that at that point most closely approximates the curve.
The curvature's reciprocal, R, is the radius of curvature in differential geometry. It is equal to the radius of the circular arc that, at that moment, most closely resembles the curve for a curve. The radius of curvature for surfaces is the diameter of a circle that, individually or in combination, best fits a normal section.
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if you have a sharper curve and youa re 60 mph if you decrease the radius of an object traveling in a circle, but keep the velocity the same, what happens to the centripetal acceleration experienced by the object?
Given a constant speed, the centripetal acceleration of an item travelling in a circle is inversely proportional to the radius of the curve (a=v2/r).
As a result, the acceleration is smaller for a gradual curve with a large radius and greater for a sharp curve with a short radius.
Centripetal acceleration: What is it?The speed at which a body rotates around a circle is known as centripetal acceleration. When a body moves in a circle, its d is equal to its velocity since velocity is a vector quantity (i.e., it has both a magnitude, the speed, and a direction) direction is continually changing, which causes a change in velocity, which results in an acceleration.
What is the centripetal acceleration's direction?The acceleration is brought about by a force that is focused at the, It is referred to as a centripetal force.
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two objects were lifted by machine. one object had a mass of 2kg, and was lifted at a speed of 2m/s. the other had a mass of 4kg and was lifted at a rate of 3m/s. Which object had more potental energy while it was being lifted a distance of 10 meters?
The object having mass 4kg will have greater potential energy as it has larger mass.
What is potential energy ?
Potential energy is a form of stored energy that is dependent on the relationship between different system components. A spring's potential energy rises when it is compressed or stretched. If a steel ball is raised above the ground as opposed to falling to the ground, it has more potential energy. It is capable of performing more work when raised. Potential energy is a characteristic of systems rather than of particular bodies or particles; for instance, the system made up of Earth and the elevated ball has more potential energy as they become further apart.
U=m g h
The object having mass 4kg will have greater potential energy as it has larger mass.
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A force of 30.ON is acted on a block of mass 15.0kg placed on a horizontal surface but the boxdoes not move. Calculate the magnitude of the frictional force between the surfaces when theapplied force is along the horizontal and when it makes angle 60° with the horizontal.
We will have the following:
1. In the first case, we will calculate the normal force:
[tex]N=(15\operatorname{kg}\cdot9.8m/s^2)\Rightarrow N=147N[/tex]Then, we will have that the fricion coefficient will be:
[tex]\mu_f=\frac{30.0N}{147N}\Rightarrow\mu_f=\frac{10}{49}\Rightarrow\mu_f\approx0.20[/tex]So the magnitude of the friccional force when applied horizontally will be of 30.0N.
2. And the magnitude when applied horizontal but the block is on an inclined surface of 60°, we will have that:
[tex]F=(10/49)(15.0\operatorname{kg}\cdot9.8m/s^2)\cos (60)\Rightarrow F=15N[/tex]So, the friction force when the force is applied, is 15N.
it takes 5 seconds to change his velocity from 30 m/s to 40 m/s, what is his acceleration? 8) jack and tom are skiing down two separate incline planes. jack is a better skier, so he is on the incline making a larger angle to the horizontal. who experiences more acceleration along the slope? (ignore friction)
In mechanics, acceleration refers to the rate at which an object's velocity with respect to time varies. The acceleration is 8.
What is acceleration?In mechanics, acceleration is the rate at which an object's velocity varies with respect to time. They are vector quantities and accelerations. The acceleration of an object is determined by the direction of the net force acting on it.Acceleration is the rate at which the speed and direction of a moving object change over time. Acceleration is defined as the rate at which something moves faster or slower. Because the direction of motion on a circle changes all the time, even when the speed remains constant.Acceleration is defined as the rate at which velocity changes over time. It is also known as an increase in velocity per second. The SI unit of acceleration is the meter per second squared, abbreviated as ms2.Therefore,
Acceleration = 40/5 = 8
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a car has two headlights, and their power is derived from the car's battery. the filament in one burns out, but the other headlight stays on. are the headlights connected in series or in parallel?
It is necessary to collimate the light source before using the prisim to disperse the light so that the light rays entering the prisim are parallel series.
What is colimate?
collimator is a tool for converting a point source's divergent radiation into a parallel beam. To perform specific measurements in spectroscopy, geometrical optics, and physical optics, the light must be collimated.
An optical collimator is made up of a tube with a convex lens at one end and a variable aperture at the other end that is located in the lens' focal plane. To examine the image without parallax, radiation entering the aperture exits the collimator as a parallel beam.
Therefore collimation is needed for the light rays entering the prism to be parallel .
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Calculate the magnitude of the resultant velocity of a pair of 100 km/h velocity vectors that are at right angles to each other
The magnitude of the resultant velocity of a pair of 100 km/h velocity vectors that are at right angles to each other is 141.42 km/h.
What is velocity?When an item is moving, its velocity is the rate at which its direction is changing as seen from a certain point of view and as measured by a specific unit of time.
Given that in the question velocity of a pair of 100 km/h velocity vectors that are at right angles to each other,
Resultant velocity,
v = [tex]\sqrt{v^{2} +v^{2} }[/tex]
= [tex]100\sqrt{2}[/tex]
= 141.42 km/h
The resultant velocity of a pair of 100 km/h velocity vectors that are at right angles to each other is 141.42 km/h.
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What is the equation for momentum (p)?
Answer:
p(momentum) = mass(kg) x velocity (m/s)
why does the sky appear blue in the day vs. red during sunset? I’m looking for an answer that explain s using light rays!!
Rayleigh scattering makes the sky appear blue in the day and red during sunset.
A clear, cloudless daytime sky is blue because molecules in the air scatter blue light from the sun more than red light. Sun at sunset, appears red or orange because blue light is scattered from your line of sight.
The white light of the sun is a mixture of all the colors of the rainbow. This was demonstrated by Isaac Newton by using a prism to separate different colors to form a spectrum. Colors of light are distinguished by different wavelengths.
The visible portion of the spectrum ranges from red light with a wavelength of about 720 nm to violet with a wavelength of about 380 nm, with orange, yellow, green, blue, and indigo in between. Her three types of color receptors in the retina of the human eye are most responsive to red, green and blue wavelengths, giving us color vision.
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a young weightlifter raises a weight from a height of 0.6 m to a height of 1.3 m in a time of 3.2 seconds. his applied force has put out an average power of 43 w. if the weight does not accelerate at all in the process, what must be its mass?
The mass is 20.038 Kg.
Mass is the amount of count in a physical body. it's also a degree of the frame's inertia, the resistance to acceleration while a net pressure is carried out. An item's mass additionally determines the power of its gravitational attraction to different bodies. The SI base unit of mass is the kilogram.
F = mg
Displacement of weight = h
= 0.7 m
work done by weight lifter W = F × h
W = (mgh)
= 0.7mg
work done in 3.2 seconds
power P = W/Δt = 0.7 mg/3.2
Given,
P = 43 W = 43 J/s
⇒ 0.7 mg/3.2 = 43 j/s
⇒ M = (43 × 3.2)/(0.7 × 9.8)
M = 20.038 Kg ans.
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Given a block which is at rest on a perfectly flat smooth surface with no friction. You push with your hand horizontally on the block with some force. If the force on the block= 4.00 N and the block moves a distance of 2.00 m on the table, then what is the work done on the block? A) 1.29 JB) 8.00 JC) 9.31 JD) 3.65 JE) 4.57 J
ANSWER
B) 8.00 J
EXPLANATION
Given:
• The force applied to move the block, F = 4.00N
,• The distance the block is moved, d = 2.00 m
Unknown:
• The work done on the block, W
If there is no friction between the block and the table, the only force acting upon the block in the direction of movement is the applied force F. Since the force is applied in the direction of movement, then the angle between the force and the displacement is 0, so the work done on the block is,
[tex]W=F\times d=4.00N\times2.00m=8.00J[/tex]Hence, the work done on the block is 8.00 J.
you are designing a diving bell to withstand the pressure of seawater at a depth of 210 m. part a what is the gauge pressure at this depth? (you can ignore changes in the density of the water with depth.)
The gauge pressure at the depth of 210 m will be 2.11974 x 10^{6} Pa .
What is gauge pressure ?
The amount of pressure measured in relation to the applied atmospheric pressure is known as gauge pressure. A diaphragm sensor can be used to measure gauge pressure, with one side of the diaphragm exposed to the pressure medium that has to be measured and the other exposed to the surrounding atmospheric pressure.
The pressure from the weight of the atmosphere is included in gauge pressure readings because gauge pressure is zero-referenced against ambient air (or atmospheric) pressure. This indicates that gauge pressure varies in response to both weather and height above sea level. Gauge pressure measurement is adequate for the majority of industrial applications because every operation in a refinery or manufacturing facility operates at the same air pressure.
The gauge pressure is ;
P = density x g x depth
where , density is of sea water .
Calculate the gauge pressure as -:
P = density x g x depth
= (1030 kg/m^{3})(9.8 m/s^{2})(210 m)
= 2.11974 x 10^{6} Pa .
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a spotlight on the ground is shining on a wall away. if a woman tall walks from the spotlight toward the building at a speed of how fast is the length of her shadow on the building decreasing when she is from the building?
His shadow is shortening at a rate of dy/dt = 0.6m/s at the time.
What is triangle total degrees?The triangle's three angles add up to a total of 180 degrees
The individual is standing at point D and has his head at point E at the time indicated in the problem.
At that moment, his shadow is visible on the wall at y = BC.
The two right triangles ABC and ADE both contain similar triangles. The ratios on their respective sides in the similar triangles are equal:
AD/AB = DE/BC
8/12 = 2/y
y = 3
If we suppose that the man is x distance from the building, then the distance from the spotlight to the man is 12 x.
12-x/12 = 2/y
1-1/12x = 2 1/y
Let's take derivatives of both sides:
-1/12dx = -2 .1/y²dy
Divide both sides by dt as follows.
-1/12.dx/dt = 2/y²dy/dt
At the time specified:
dx/dy = 1.6m/s
y = 3
Let's connect them
- 1/2 (1.6) = -2.9 dy/dt
dy/dt = 1.6/12×9/2 = 0.6m/s.
At the time in question, this is the pace at which his shadow's length is shortening.
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The complete question is:
"A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?"
Question 6:A particle of mass 0.2 kg is moving in a straight line at speed 2.5ms, a constant force of magnitude FN is applied to it in the direction in which it is moving. The speed of the particle 5 seconds later is 4.5ms Find the value of F, magnitude of the force applied.
First, let's calculate the particle acceleration, using the formula below:
[tex]\begin{gathered} V=V_0+a\cdot t \\ 4.5=2.5+a\cdot5 \\ 5a=4.5-2.5 \\ 5a=2 \\ a=\frac{2}{5}=0.4\text{ m/s}^2 \end{gathered}[/tex]Now, to find the force applied, let's use the second law of Newton:
[tex]\begin{gathered} F=m\cdot a \\ F=0.2\cdot0.4 \\ F=0.08\text{ N} \end{gathered}[/tex]Therefore the value of F is 0.08 N.