Question

a rock falls from a height of 80 feet. write an equation that gives the height of the rock (in feet) above the ground as a function of time (in seconds) and find how many seconds it will take for the rock to hit the ground.
let h(t) = 0 and solve h = -16t² + 80

about 6.1 seconds
about 8.2 seconds
about 2.2 seconds
about 4.7 seconds

Explanation:

Step1: Set up the equation

We know the height function is \( h = -16t^{2}+80 \), and we want to find when the rock hits the ground, so we set \( h = 0 \). So the equation becomes \( 0=-16t^{2}+80 \).

Step2: Solve for \( t^{2} \)

First, we can rearrange the equation to isolate \( t^{2} \). Add \( 16t^{2} \) to both sides: \( 16t^{2}=80 \). Then divide both sides by 16: \( t^{2}=\frac{80}{16} = 5 \).

Step3: Solve for \( t \)

Take the square root of both sides. Since time cannot be negative in this context, we consider the positive square root. So \( t=\sqrt{5}\approx2.2 \) (because \( \sqrt{5}\approx2.236 \), which is approximately 2.2).

Answer:

about 2.2 seconds