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 up the equation

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

Step2: Rearrange the equation

Add $16t^{2}$ to both sides: $16t^{2}=7744$.

Step3: Solve for $t^{2}$

Divide both sides by 16: $t^{2}=\frac{7744}{16}=484$.

Step4: Solve for $t$

Take the square - root of both sides. Since $t\geq0$ (time cannot be negative in this context), $t=\sqrt{484}=22$.

Answer:

22