Question

A ball is launched into the sky at 272 feet per second from the roof of a skyscraper 1,344 feet tall. The equation for the ball’s height h at time t seconds is h = -16t2 + 272t + 1344. When will the ball strike the ground?

Answer 1

The answer is -16(t+4)(t-21)

Answer 2

Time taken to reach the ball to the ground is 21 seconds.

Explanation:

Given : A ball is launched into the sky at 272 feet per second from the roof of a skyscraper 1,344 feet tall. The equation for the ball’s height h at time t seconds is
`h = -16t^2 + 272t + 1344`.

To find : When will the ball strike the ground?

Solution :

The equation for the ball's height 'h' at time 't' is given by,

`h(t)= -16t^2 + 272t + 1344`

When the ball strike the ground the height of the ball became zero.

Substitute h=0 in the given equation,

`-16t^2 + 272t + 1344=0`

Taking 16 common,

`16(-t^2 + 17t + 84)=0`

or
`t^2-17t-84=0`

Solve by middle term split,

`t^2-21+4t-84=0`

`t(t-21)+4(t-21)=0`

`(t-21)(t+4)=0`

`t=21,-4=0`

Reject t=-4 as time can never be negative.

Therefore, Time taken to reach the ball to the ground is 21 seconds.