Question

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?
​

Answer 1

A- 150

B- 3.05

Explanation:

Answer 2

a) 150ft

b) 3.05s

EXPLANATION.

The quadratic function that models the height of the ball is

`h(t) = - 16.1{t}^(2) + 150`

The ball was dropped at time t=0.

We plug in t=0 into the given function to get,

`h(0) = - 16.1{(0)}^(2) + 150`

`h(0) = 150`

Therefore the ball was dropped from a height of 150 ft.

When the ball hit the ground, then h(t)=0.

This implies that:

`- 16.1{t}^(2) + 150=0`

`- 16.1{t}^(2) =- 150`

`{t}^(2) =(- 150)/(-16.1)`

We take square root of both sides,

`{t} =√(9.317)`

`{t} =3.05` to the nearest hundredth.

Therefore the ball hit the ground after approximately 3.05 seconds.