Question

A bullet is shot straight upward with an initial speed of 925 ft/s. The height of the bullet after t seconds is modeled by the function h(t) = −16t2 + 925t where h is measured in feet. Use the function h to find the average speed of the bullet during the given time intervals

Answer 1

462 ft/s

Explanation:

The height of the bullet is modeled by:

h(t) = -16t² + 925t------------------------------------ (1)

The speed of the bullet is modeled by the first derivative of equation (1)

dh/dt= -32t + 925------------------------------------ (2)

At maximum height, dh/dt = 0

0 = -32t + 925

32t = 925

t = 925/32

= 28.91 seconds

This means that the total time to reach maximum height is 28.91 seconds

Substituting into equation (1) we can calculate the maximum height:

h = -16 (28.91)² +925 (28.91)

= -13,372.61 + 26,742.675

= 13,367.065 ‬ft

Average speed = Total distance/ Total time

= 13,367.065/28.91

= 462.368

≈ 462 ft/s