Question

A model rocket is launched from a raised platform 72 feet off the ground at an initial velocity of 96 ft/sec. Write the function s(t) that models the height of the rocket in feet after t seconds.

Answer 1

The function that models the height of the rocket after t seconds is s(t) = -16t² + 96t + 72, taking into account the initial velocity of 96 ft/s, initial height of 72 feet, and the acceleration due to gravity.

Step-by-step explanation:

To determine the function s(t) that models the height of the rocket after t seconds, we can use the kinematic equation for vertical motion under gravity. Assuming the acceleration due to gravity is 32 ft/s² downwards, the initial velocity is upward at 96 ft/s, and the rocket starts from a platform 72 feet above ground level, we have:

s(t) = -16t² + 96t + 72

This equation takes into account the initial position and velocity, as well as the acceleration due to gravity (which is negative because it is directed downwards). The term -16t² represents the displacement due to the acceleration of gravity (half of 32 ft/s²), 96t is the initial velocity component, and 72 is the height of the platform from where the rocket was launched.