Question

A bouncy ball is dropped from a height of `144` feet. The function `h=−16x^2+144` gives the height, `h`, of the ball after `x` seconds. When does the ball hit the ground?

Answer 1

The ball will hit the ground in `3` secs.

Explanation:

`16x^2` must equal `+144` so that `h = 0`.

In other words, when the ball hits the ground, the distance above the ground will be zero.

That occurs `3` seconds after the ball was released.

`0=-16x^2 +144`

`16x^2 =144`

Answer 2

`3` seconds

Explanation:

`h(x)=-16x^2+144` => the ball hits the ground at h = 0:
`-16x^2+144=0`
`-16(x^2-9)=0`
`x^2=9`
`x=+-3` => reject the negative time, thus:
`x=3` the ball hits the ground 3 seconds after it was dropped

Answer 3

The ball hits the ground after `3` seconds.

Explanation:

When the ball is dropped, the height will get less and less. When it hits the ground the height will be `0`

`0 = -16x^2 +144" "larr` now solve the equation,

You can isolate the `x` term:

`0 = -x^2 +9" "larr div 16`

`x^2 = 9`

`x =+-sqrt 9`

`color(blue)(x = +3) or x=-3`

You could also factorise:

`0 =144-16x^2" "larr` difference of two squares.

`0 = 9-x^2" "larr div 16`

`0 = (3+x)(3-x)`

`x= -3 or color(blue)(x=+3)`

In each case reject `-3` because the time cannot be negative,