Question

a thermometer falls from a weather balloon at a height of 7,744 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 thermometer to hit the ground?

Explanation:

Step1: Set height to 0

When the thermometer hits the ground, $h(t)=0$. The initial height is 7744 ft, so the equation becomes $0=-16t^{2}+7744$.

Step2: Rearrange the equation

$16t^{2}=7744$.

Step3: Solve for $t^{2}$

$t^{2}=\frac{7744}{16}=484$.

Step4: Solve for $t$

$t = \sqrt{484}=22$ (we take the positive value since time cannot be negative).

Answer:

22