Question

A rocket is fired straight up with an initial velocity of 256 ft/s. The rocket is fired from a platform that is 576 feet above the ground. Use 16 for g.

Write a function, s(t), that models the height of the rocket at time t seconds. This rocket reaches a maximum height of 1600 ft; use this fact to validate your model.
a) s(t) = -16t^2 + 256t + 576
b) s(t) = 16t^2 + 256t + 576
c) s(t) = -16t^2 + 256t - 576
d) s(t) = 16t^2 + 256t - 576

Answer 1

The function that models the height of the rocket at time t seconds is s(t) = -16t² + 256t + 576. This function can be validated by checking if it reaches a maximum height of 1600 ft.

Step-by-step explanation:

The function that models the height of the rocket at time t seconds is s(t) = -16t² + 256t + 576.

To find the function, we use the equation of motion for the rocket: s(t) = s_0 + v_0t + ½ a t^2, where s(t) is the height of the rocket at time t, s_0 is the initial height of the rocket, v_0 is the initial velocity of the rocket, and a is the acceleration due to gravity.

Plugging in the given values, we get s(t) = -16t² + 256t + 576.

This function can be validated by checking if it reaches a maximum height of 1600 ft.