Answer:
(a) h = 23.34 m
(b) W = - 33.2 J
(c) W = 0 J
Step-by-step explanation:
(a)
We will use the third equation of motion to find out the height reached by the ball:

where,
g = acceleration due to gravity = - 9.81 m/s² (-ve sign due to upward motion)
h = height reached by ball = ?
vf = final speed = 0 m/s
vi = initial speed = 21.4 m/s
Therefore,

h = 23.34 m
(b)
The work done by gravity on the ball will be equal to its potential energy:
W = mgh
where,
W = Work done = ?
m = mass of ball = 0.145 kg
Therefore,
W = (0.145 kg)(- 9.81 m/s²)(23.34 m)
W = - 33.2 J
(c)
The total work done will be the sum of the work done during upward and downward motion. Here the magnitude of the work done during upward motion will be the same as the magnitude of the work done during downward motion with opposite direction. Therefore,
W = -33.2 J + 33.2 J
W = 0 J