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)
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
