Question

3. During a physics class, students are working on a project thatmeasures a trajectory of a projectile fired straight upward in terms of itdistance d (in feet) above the ground over the t seconds. The teacherprovides the student with the following function that models the scenaricd(t) = -16t? + 400t. What is the maximum height the projectile can reachgiven the equation?a.The maximum height is 2,496 feet at 12 secondsb. The maximum height is 2,500 feet at 12.5 secondsC.The maximum height is 2,496 feet at 13 secondsaThe maximum height cannot be determined from the function

Answer 1

Solution:

The maximum height, d, in feet is modeled by;

$d(t)=-16t^2+400t$

At maximum height,

$\begin{gathered} d^{\prime}(t)=(-16\times2)t^{2-1}+(400\times1)t^{1-1}=0 \\ \\ d^{\prime}(t)=-32t+400=0 \end{gathered}$

Then, we would solve for t at maximum height;

$\begin{gathered} -32t+400=0 \\ \\ 32t=400 \\ \\ t=\frac{400}{32} \\ \\ t=12.5 \end{gathered}$

Thus, the maximum height is;

$\begin{gathered} d(12.5)=-16(12.5)^2+400(12.5) \\ \\ d(12.5)=2500 \end{gathered}$

CORRECT OPTION: The maximum height is 2,500 feet at 12.5 seconds.