### Home > CALC > Chapter 5 > Lesson 5.1.1 > 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. Homework Help ✎

Start with the basic equation: *s*(*t*) = −16*t*² + *v*_{0}*t* + *s*_{0} where *v*_{0} is the initial velocity and *s*_{0} is the initial height of the rocket from the ground.

The initial height of the rocket is 0 because it is shot from the ground.

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

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 = −32*t* +182