parabolas word problem

Question

The function y=-16^2+40 represents the height y(in feet) of a water droplet t seconds after falling from an icicle.

a.After how many seconds does the water droplet hit the ground? Round your answer to two decimal places. b.A second water droplet falls from a height of 22 feet. Which water droplet hits the ground in the least amount of time? Explain.

Answer 1

y=-16t^2 +40 usually means 40 feet is the initial position

set y=0 = -16t^2 +40

t^2 = 40/16 =5/2 = 2.5

t =sqr2.5

t = about 1.58 seconds to reach the ground

a second droplet starting at 22 feet will hit the ground faster

0 = -16t^2 + 22

t^2 = 22/16 = 11/8

t = sqr(11/8)

r = about 1.17 seconds to hit the ground