Chapter 14, Problem 38RE

Instantaneous Velocity of a Ball In physics it is shown that the height $s$ of a ball thrown straight up with an initial velocity of $96\text{ft/sec}$ from a rooftop $112$ feet high is

$s=s\left(t\right)=-16t^2+96t+112$ where $t$ is the elapsed time that the ball is in the air. The ball misses the rooftop on its way down and eventually strikes the ground.

When does the ball strike the ground? That is, how long is the ball in the air?

At what time $t$ will the ball pass the rooftop on its way down?

What is the average velocity of the ball from $t=0$ to $t=2$?

What is the instantaneous velocity of the ball at time $t$?

What is the instantaneous velocity of the ball at $t=2$?

When is the instantaneous velocity of the ball equal to zero?

What is the instantaneous velocity of the ball as it passes the rooftop on the way down?

What is the instantaneous velocity of the ball when it strikes the ground?