Question

modeling with mathematics 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 = -16t^2 + 24 ) represents the height ( h ) (in feet) of the sunglasses after ( t ) seconds. how long does it take the sunglasses to hit the ground, rounded to the nearest tenth? it takes the sunglasses about (square) seconds to hit the ground.

Explanation:

Step1: Set height to 0

We need to find when the sunglasses hit the ground, so set \( h = 0 \) in the function \( h=- 16t^{2}+24 \).
\( 0=-16t^{2}+24 \)

Step2: Solve for \( t \)

First, rearrange the equation:
\( 16t^{2}=24 \)
Then, divide both sides by 16:
\( t^{2}=\frac{24}{16}=\frac{3}{2} \)
Take the square root of both sides (we consider the positive root since time can't be negative):
\( t = \sqrt{\frac{3}{2}}\approx1.2 \) (rounded to the nearest tenth)

Answer:

\( 1.2 \)