Question

a camera is accidentally dropped from a helicopter at a height of 4,096 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 camera to hit the ground?

Explanation:

Step1: Set height to 0

When the camera hits the ground, $h(t)=0$. The initial height is 4096 ft, so the equation becomes $0=-16t^{2}+4096$.

Step2: Rearrange the equation

Add $16t^{2}$ to both sides: $16t^{2}=4096$.

Step3: Solve for $t^{2}$

Divide both sides by 16: $t^{2}=\frac{4096}{16}=256$.

Step4: Solve for $t$

Take the square - root of both sides. Since $t$ represents time and cannot be negative in this context, $t = \sqrt{256}=16$.

Answer:

16