# Related rates falling rock with shadow

## Homework Statement

a light shines from the op of a pole 50ft high a ball is dropped from the same height from a point 30 feet away from the light , how fast is the shadow of the ball moving along the ground .5second later.

So is the ball falling at 32ft/s^2
would we set it up like 50/x=y/(x-30)
x is the distance from the light pole to the end of the shadow and y is the heidght of the ball above the ground . is the balls rate 32t then we would take the deravative and plug every thing in , is my setup right .

tiny-tim
Homework Helper
Hi cragar!
a light shines from the op of a pole 50ft high a ball is dropped from the same height from a point 30 feet away from the light , how fast is the shadow of the ball moving along the ground .5second later.

would we set it up like 50/x=y/(x-30)
x is the distance from the light pole to the end of the shadow and y is the heidght of the ball above the ground . is the balls rate 32t then we would take the deravative and plug every thing in , is my setup right .

Yes, that's fine!

Just one improvement …

you've used similar triangles,

but since the speed is 0 at the top, it will save time if instead of y you use the height of the ball below the top, and use a different pair of similar triangles