Question

a phone is accidentally dropped from a helicopter at a height of 3,600 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 phone to hit the ground?

Explanation:

Step1: Set height to 0

When the phone hits the ground, $h(t)=0$. The initial height is 3600 ft, so the equation becomes $0=-16t^{2}+3600$.

Step2: Rearrange the equation

Add $16t^{2}$ to both sides: $16t^{2}=3600$.

Step3: Solve for $t^{2}$

Divide both sides by 16: $t^{2}=\frac{3600}{16}=225$.

Step4: Solve for $t$

Take the square - root of both sides. Since $t$ represents time and cannot be negative in this context, $t = \sqrt{225}=15$.

Answer:

15