Question

A projectile is launched upward with a velocity of 256 feet per second from the top of a 35-foot structure. What is the maximum height attained by the projectile?

Answer 1

1059 ft

Explanation:

For problems like these, we assume the acceleration due to gravity is -32 ft/s², so the velocity will decrease to zero in time t, where ...

0 = 256 -32t

32t = 256

t = (256 ft/s)/(32 ft/s² ) = 8 s

Since velocity is linearly decreasing from 256 ft/s to 0, its average value of 128 ft/s will serve to tell us the height attained.

Height attained is ...

35 ft + (128 ft/s)(8 s) = 35 ft + 1024 ft = 1059 ft

The maximum height attained by the projectile is 1059 feet.