Question

A person sitting in the top row of the bleachers at a sporting event drops a pair of sunglasses from a height of 24 feet. the function h=−16x2+24h=−16x2+24 represents the height hh (in feet) of the sunglasses after xx seconds. how long does it take the sunglasses to hit the ground, rounded to the nearest tenth?

Answer 1

It takes
`1.2s` to hit the ground.

Explanation:

We have the following function that models the situation :

`h(x)=-16x^(2)+24`

Where ''h'' represents the height in feet and ''x'' represents the time in seconds.

When the sunglasses hits the ground, its height is
`0ft`.

We can replace
`h(x)` by
`0` and calculate the value of ''x'' that verifies the expression (its unit will be seconds) ⇒

`0=-16x^(2)+24`

`-24=-16x^(2)`

`x^(2)=1.5`

`x=√(1.5)=1.2247` (We know that
`x\geq 0` because a negative value of time is absurd)

1.2247 rounded to the nearest tenth is 1.2

Finally, we found out that the sunglasses will hit the ground in
`1.2` seconds.

Answer 2

This graph is a negative parabola. The ground is at a height of 0, so set h=0 and solve for x.
0 = -16x²+24
16x² = 24
x² = 24/16 = 1.5
x = +/-√1.5 ≈ +/- 1.2
Since x represents time, the negative answer is not valid (unless you have a time machine and can go backwards in time).
So, it takes ≈ 1.2 seconds for the sunglasses to hit the ground.