CPM Homework Help : CALC Problem 5-9

The Math Booster Club shot a rocket from the ground straight up into the air to celebrate $π$ Day. The launcher shot the rocket with a starting velocity of $182$ ft/sec. Find a function $s(t)$ for the height of the rocket. Then find its maximum height and the amount of time it was in the air.

Hint 1:

Start with the basic equation: $s(t) = −16t^² + v_0t + s_0$ where $v_0$ is the initial velocity and $s_0$ is the initial height of the rocket from the ground.

Hint 2:

The initial height of the rocket is $0$ because it is shot from the ground.
To find the maximum height, take the derivative of the function and set it equal to zero because the maximum height occurs when the velocity is zero.
$0 = −32t +182$

Answer:

The initial velocity is $182$ ft/sec. Thus: $s(t) = −16t^2 + 182t$