(a)

Height function of the ball is .

The velocity function is the derivative of position function.

.

Ball reaches its maximum height when the velocity is zero.

Therefore ball will reach maximum height when  seconds.

Find the maximum height by substituting  in .

Thus, the maximum height of the ball is  ft.

(b)

When height of the ball is  ft determination of velocity:

Find the time when .

Height function is .

Substitute  in the above expression.

 and .

Find the velocity when :

 m/sec.

Velocity of the ball is  m/sec when it is  ft above the ground on its way upwards.

Find the velocity when  :

 m/sec.

Here the negative sign indicates that direction of motion is downwards.

Velocity of the ball is  m/sec when it is  ft  above the ground on its way downwards.

(a) The maximum height of the ball is  ft.

(b) Velocity of the ball is  m/sec when it is  ft  above the ground on its way upwards.

Velocity of the ball is  m/sec when it is  ft  above the ground on its way downwards.