Question

The height, s, of a ball thrown straight down with initial speed 32 ft/sec from a cliff 48 feet high is s(t) = -16t2 - 32t + 48, where t is the time elapsed that the ball is in the air. What is the instantaneous velocity of the ball when it hits the ground?

Answer 1

you should first of all find the time that takes for the ball to hit the ground
for that find t when s(t) = 0

Answer 2

use first derivative to find an expression for instantaneous velocity since \(v(t) = \frac{d[s(t)]}{dt}\) use the above found time to find the answer