Kinematic question?

Method 1:
(i)
The ball hits the floor and rebounds with half the speed it had just prior to impact.
As K.E. = (1/2)mv², the ball rebounds with a quarter of kinetic energy.

When the ball first time hits the ground, K.E.
= Loss in P.E.
= mg(16)
= 16 mgh

After first bounce, Gain in P.E. = Loss in K.E.
mgh = (1/4) (16 mgh)
Greatest height after the first bounce = 4 m

(ii)
Similarly, greatest height after the second bounce = (1/4) (4) = 1 m

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Method 2:
(i)
Take g = 9.8 m/s²
Assign all upward quantities as positive and all downward quantities as negative.

Consider that the ball falls to the ground from a height of 16 m:
v² = u² + 2as
v² = 0² + 2(-9.8)(-16)
Velocity when the ball hits the ground, v = 17.7 m/s

Consider the first bounce:
v² = u² + 2as
0 = (17.7/2)² + 2(-9.8)(s)
Greatest height after the first bounce, s = 4.0 m

(ii)
Consider that the ball falls to the ground from a height of 4.0 m:
v² = u² + 2as
v² = 0² + 2(-9.8)(-4)
Velocity when the ball hits the ground, v = 8.85 m/s

Consider the first bounce:
v² = u² + 2as
0 = (8.85/2)² + 2(-9.8)(s)
Greatest height after the second bounce, s = 1.0 m