The quadratic function h(t) = -16.1t2 + 150 models a ball's height, in feet, over time, in seconds,after it is dropped from a 15 story building.From what height, in feet, was the ball dropped?After how many seconds, rounded to the nearest hundredth, did the ball hit the ground?
Accepted Solution
A:
ANSWERa) 150ftb) 3.05sEXPLANATION.The quadratic function that models the height of the ball is [tex]h(t) = - 16.1{t}^{2} + 150[/tex]The ball was dropped at time t=0.We plug in t=0 into the given function to get,[tex]h(0) = - 16.1{(0)}^{2} + 150[/tex][tex]h(0) = 150[/tex]Therefore the ball was dropped from a height of 150 ft.When the ball hit the ground, then h(t)=0.This implies that:[tex]- 16.1{t}^{2} + 150=0[/tex][tex]- 16.1{t}^{2} =- 150[/tex][tex]{t}^{2} =\frac{- 150}{-16.1}[/tex]We take square root of both sides,[tex]{t} =\sqrt{9.317}[/tex][tex]{t} =3.05[/tex] to the nearest hundredth.Therefore the ball hit the ground after approximately 3.05 seconds.