a child drops a rock off a building that is 64 feet tall. if the equation for height as a function of time…

a child drops a rock off a building that is 64 feet tall. if the equation for height as a function of time is h(t) = -16t² + initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the rock to hit the ground? ? seconds

Answer

Explanation:

Step1: Set height to 0

When the rock hits the ground, $h(t)=0$. The initial height is 64 feet, so the equation becomes $0 = - 16t^{2}+64$.

Step2: Rearrange the equation

Add $16t^{2}$ to both sides: $16t^{2}=64$.

Step3: Solve for $t^{2}$

Divide both sides by 16: $t^{2}=\frac{64}{16}=4$.

Step4: Solve for $t$

Take the square - root of both sides. Since $t$ represents time and cannot be negative in this context, $t = \sqrt{4}=2$.