Question

A ball is launched out of a cannon that is 24 feet off the ground. The height of the ball after "t" seconds is represented by

h(t) = -16t² + 20x + 24
How many seconds will it take for the to reach the ground?

Answer 1

Given:

The height of ball is represented by the below function:

`h(t)=-16t^2+20t+24`

To find:

The number of seconds it will take to reach the ground.

Solution:

We have,

`h(t)=-16t^2+20t+24`

At ground level, the height of ball is 0, i.e.,
`h(t)=0`.

`-16t^2+20t+24=0`

Taking out greatest common factor.

`-4(4t^2-5t-6)=0`

`4t^2-5t-6=0`

Splitting the middle term, we get

`4t^2-8t+3t-6=0`

`4t(t-2)+3(t-2)=0`

`(t-2)(4t+3)=0`

Using zero product property, we get

`(t-2)=0` and
`(4t+3)=0`

`t=2` and
`t=-(3)/(4)`

Time cannot be negative, so
`t=2`.

Therefore, the ball will reach the ground after 2 seconds.