(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.