(a) 168.2 ft/s
The vertical position of the ball is given by
where t is the time.
By differentiating this expression, we find the velocity:
The maximum height is reached when the velocity is zero, so:
From which we find
And substituting this value into the equation for s, we find the maximum height:
(b) 16 ft/s
We want to find the velocity of the ball when the position of the ball is
s = +320 ft
Substituting into the equation for the position,
Solving for t, we find two solutions:
t = 4 s
t = 5 s
The first one corresponds to the instant in which the ball is still on its way up: Substituting into the equation for the velocity, we find the velocity of the ball at that time
(c) -16 ft/s
Now we want to find the velocity of the ball when the position of the ball is
s = +320 ft
but on its way down. In the previous part, we found
t = 4 s
t = 5 s
So the second time corresponds to the instant in which the ball is at s = 320 ft but on the way down.
Substituting t = 5 s into the equation for the velocity, we find:
And the negative sign means the direction is downward.