What is the speed of the shadow on the wall when a horse runs in a circle?

In summary, the problem involves a horse running in a circle with constant velocity and a flashlight in the center, lighting in all directions. A wall is placed as a tangent to the circle. The question asks for the speed of the shadow on the wall as the horse runs from the tangential point and passes 1/8 of the circle. The attempt at a solution involves using the equations for velocity, distance, and acceleration to determine the speed of the shadow. However, the assumption of constant acceleration may not be valid as the distance of the shadow will approach infinity when the angle is π/2. A vector representation of the velocities of the horse and the shadow could be helpful in solving the problem.
  • #1
acko
3
0

Homework Statement


Horse is running in circle with constant velocity V. In the middle of circle is flashlight, lighting in all directions. Wall is set as a tangent to circle. If horse starts running from tangential point and pass 1/8 of circle, what will be speed of a shadow on the wall? Can someone help me solve this? Will acceleration of shadow be constant?

Homework Equations


V-velocity of horse
R-radius of circle
Vs-velocity of shadow
t-time of distance traveled by horse and shadow

The Attempt at a Solution


Because V is constant, time of distance traveled of horse is t=πR/4V.
Distance traveled for shadow is R (radius of circle).
Initial velocity of shadow is V.
So if acceleration of shadow is constant: R=V*t +a*t² /2
Acceleration is equal to (Vs-V)/t
My solution is Vs=V(8/π-1).
 
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  • #2
I think it is a bad assumption that the acceleration of the shadow is constant because by the time the angle is π/2, the shadow's distance will be infinite. Well, I am assuming it is a straight wall, because the problem statement said that it was "set as a tangent to circle".

P.S. Welcome to Physics Forums.
 
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Likes acko
  • #3
Try to draw a vector representation the velocity of the shadow and the velocity of the horse and how they are related in terms of the angle rotated. I think if you can do that it will help a lot.
 
  • #4
TomHart said:
Try to draw a vector representation the velocity of the shadow and the velocity of the horse and how they are related in terms of the angle rotated. I think if you can do that it will help a lot.
thanks
 
  • #5
I tried but I can't solve this problem. Can someone explain me?
 
  • #6
acko said:
I tried but I can't solve this problem. Can someone explain me?
By the forum rules we can't provide a solution or do the work for you. We can point out flaws in your work or offer corrections or suggestions on how to think about the problem or things to investigate.

Can you post your sketch of the problem?

A hint: Consider the angular velocity of the line connecting the light, the horse, and the wall.
 
  • #7
Vectors form isosceles triangle with two 45 degrees angles and one 90. So Vs=√2*V. That sounds too simple.
 

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FAQ: What is the speed of the shadow on the wall when a horse runs in a circle?

What is horse kinematics?

Horse kinematics is the study of the movement and motion of horses. It involves analyzing the forces, angles, and velocities that affect a horse's gait and posture.

Why is understanding horse kinematics important?

Understanding horse kinematics is important for many reasons. It can help improve horse racing and sports performance, as well as prevent injuries in horses. It can also aid in the design of equipment and training programs for horses.

What factors affect horse kinematics?

Several factors can affect horse kinematics, including genetics, conformation, training, and the type of terrain the horse is moving on. Other factors, such as rider weight, can also have an impact.

How is horse kinematics studied?

Horse kinematics is studied using various tools and techniques, including high-speed cameras, motion capture technology, force plates, and accelerometers. These tools allow researchers to track and measure the horse's movements and analyze the data to understand the mechanics of their motion.

What are some common issues with horse kinematics?

Some common issues with horse kinematics include lameness, asymmetry, and poor gait mechanics. These issues can impact a horse's performance and overall health. Understanding horse kinematics can help identify and address these issues for the well-being of the horse.

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