Question

a quarter falls off a building that is 144 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 quarter to hit the ground? ? seconds

Explanation:

Step1: Set up the equation

When the quarter hits the ground, $h(t)=0$. The initial height is 144 feet. So the equation becomes $0 = - 16t^{2}+144$.

Step2: Rearrange the equation

Add $16t^{2}$ to both sides: $16t^{2}=144$.

Step3: Solve for $t^{2}$

Divide both sides by 16: $t^{2}=\frac{144}{16}=9$.

Step4: Solve for $t$

Take the square - root of both sides. Since $t$ represents time and cannot be negative in this context, $t = \sqrt{9}=3$.

Answer:

3