# Horse kinematics problem

1. Jan 28, 2017

### acko

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
V-velocity of horse
t-time of distance traveled by horse and shadow

3. The attempt at a solution
Because V is constant, time of distance traveled of horse is t=πR/4V.
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).

2. Jan 28, 2017

### TomHart

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.

3. Jan 28, 2017

### TomHart

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. Jan 28, 2017

### acko

thanks

5. Jan 30, 2017

### acko

I tried but I can't solve this problem. Can someone explain me?

6. Jan 30, 2017

### Staff: Mentor

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. Jan 30, 2017

### acko

Vectors form isosceles triangle with two 45 degrees angles and one 90. So Vs=√2*V. That sounds too simple.

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