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

[acko]

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).

 

[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.

 

[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.

 

[acko]

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

 

[acko]

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

 

[gneill]

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.

 

[acko]

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