Question

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)

Answer 1

The speed of the ball is
ds/dt = 32t
At t =1/2 s
ds/dt = 16 ft/s
The distance from the ground
50 - 16(1/2)^2 = 46 ft
The triangles formed are similar
50/46 = (30 + x)/x
x = 345 ft

50 / (50 - s) = (30 + x)/x
Taking the derivative and substituing
ds/dt = 16
and
Solve for dx/dt