(a)

The height function of the projectile shot is .

The velocity function is the derivative of position function.

.

The velocity function is .

Velocity after  sec :

Velocity after  sec :

(b)

Projectile reaches its maximum height when the velocity is zero.

Velocity is .

Substitute  in above expression.

(c)

The projectile reaches maximum height when  sec.

Therefore, if we substitute  in  we get the maximum height.

 m.

(d)

When projectile hits the ground the height will be equal to zero.

Solve the equation for the value of  :

.

.

Here time can not be negative, it is not consider.

Thus, the projectile hits the ground when  sec.

(e)

Velocity is .

Substitute  in above expression.

 m/sec.

(a)The velocity after  sec is  m/s and after  sec is  m/s

(b) After  sec projectile reaches its maximum height.

(c) m.

(d) The projectile hits the ground when  sec.

(e)  m/sec.