Question

a dime is dropped from a building at a height of 1,024 ft. 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 dime to hit the ground?

Explanation:

Step1: Set height to 0

$h(t)=0$, so $0 = - 16t^{2}+1024$.

Step2: Rearrange the equation

$16t^{2}=1024$.

Step3: Solve for $t^{2}$

$t^{2}=\frac{1024}{16}=64$.

Step4: Solve for $t$

$t=\sqrt{64}=8$ (we take the positive value since time cannot be negative).

Answer:

8