Help required with mechanics question. Any answers appreciated.

A ball is released from rest at a point which is 10m above a wooden floor. Each time the ball strikes the floor, it rebounds with 3/4 the speed with which it strikes the floor. Find the greatest height above the floor reached by the ball a) the first time it bounces and b) the second time.

I get the answer to the first part but I don't get why the same approach isn't needed for the 2nd part. I used the s=5.6 from the first part, u=10.5 and a=9.8. What I planned to do, like the first part is find the speed just before the ball bounces then find 3/4 of that. But I don't get why you are meant to do that for only the first part, and use the SAME speed as you got in the first part and multiply by 3/4.

I'm not FULLY sure what you tried to do here, but after it rebounds off the floor the first time with speed $u$, it will just follow some parabolic path where it goes up to the max height of 5.6m as you found in part(a) then it just comes back down with the final speed of $u$ (as a consequence of the parabolic path), so the initial speed after the 2nd rebound is $\frac{3}{4}u$ - i.e. just 0.75*(rebound speed in part A)

Thanks, but how do you know when it follows a parobolic path?

Because it's a projectile that is essentially 'launched' with speed $u$ when it rebounds for the first time, and every projectile follows a parabolic path.