Question

a skydiver drops her watch as she jumps out of a plane flying at an altitude of 6,400 feet. 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 watch to hit the ground? ? seconds

Explanation:

Step1: Set the height function to 0

When the watch hits the ground, $h(t)=0$. The initial height is 6400 feet, so the equation becomes $0=-16t^{2}+6400$.

Step2: Rearrange the equation

Add $16t^{2}$ to both sides of the equation: $16t^{2}=6400$.

Step3: Solve for $t^{2}$

Divide both sides of the equation by 16: $t^{2}=\frac{6400}{16}=400$.

Step4: Solve for $t$

Take the square - root of both sides. Since $t$ represents time, we consider the positive square - root. So $t = \sqrt{400}=20$.

Answer:

20