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

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.

Answer 2

Answer:

It takes $1.2s$ to hit the ground.

Step-by-step 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) ⇒

$0=-16x^{2}+24$

$-24=-16x^{2}$

$x^{2}=1.5$

$x=\sqrt{1.5}=1.2247$     (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.