A cliff diver plunges from a height of 100 ft above the water surface. The distance the diver falls in seconds is given by the function d(t)=16t^2.

Question

A cliff diver plunges from a height of 100 ft above the water surface. The distance the diver falls in seconds is given by the function d(t)=16t^2.

a.) after how many seconds will the diver hit the water?

b.) with what velocity does the diver hit the water?

Answer 1

d(t) = 16t^2 = 100

t^2 = 100/16

t = 10/4 = 2 1/2 seconds to hit the water

take the derivative to find velocity

v(t) = d'(t) = 32t

plug in t=2 1/2 seconds to solve for velocity

v(2.5) = 32(2.5) =80 ft/sec = 80 feet per second velocity when he hits the water