Posted by **Teri** on Friday, June 8, 2012 at 10:04am.

a light shines from the top of a pole 50ft high. a ball is dropped from the same height from a point 30 ft away from the light. how fast is the ball's shadow moving along the ground 1/2 sec later? (assume the ball falls at a distance of s=16t^2 in t sec)

- Math -
**Steve**, Friday, June 8, 2012 at 10:35am
when the ball is at height h, the shadow is at distance x from the base of the light pole. Using similar triangles,

x/50 = (x-30)/h

h = 50(x-30)/x = 50 - 1500/x

now, h = 50-s = 50-16t^2, so

dh/dt = -32t, and

h(1/2) = 50 - 16(1/4) = 46

x/50 = (x-30)/46, so x=375

-32t = 1500/x^2 dx/dt

at t = 1/2,

-16 = 1500/(140625) dx/dt

dx/dt = -1500

so, the shadow is moving toward the pole at 1500 ft/s

## Answer this Question

## Related Questions

- calc - A light is at the top of a pole 80ft high. A ball is dropped at the same ...
- math - A street light is at the top of a 15 ft pole. A 5 ft tall girl walks ...
- calculus - A light is attached to the wall of a building 64 feet above the ...
- math - A street light (light source) is 15 m above the ground. A ball is freely ...
- calculus - A ball is dropped from the same height, but 20 feet away from the ...
- Math - A street light is at the top of a 16 ft tall pole. A woman 6 ft tall ...
- Math: related rates - A street light is at the top of a 26 ft pole. A 5 ft tall...
- physics - A lightbulb emits light that creates a shadow of a ball on a wall. If ...
- physics - A man standing 15.0 ft away from a light pole which is an additional ...
- Math - A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft ...

More Related Questions