)the best rebounders in basketball have a vertical leap (that is, the vertical movement of a fixed point on their body) of about 120 cm. (a) what is their initial "launch" speed off the ground? (b) how long are they in the air?

Let u = the vertical launch speed.

Neglect air resistance, and g = 9.8 m/s².

At the maximum height of h = 120 cm = 1.2 m, the vertical velocity is zero.
Therefore
(u m/s)² - 2*(9.8 m/s²)*(1.2 m) = 0
u² = 23.52 (m/s)²
u = 4.85 m/s

The time to attain maximum height is one half of the travel time.
If t = time to attain maximum height, then
u - gt = 0
4.85 - 9.8t = 0
t = 4.85/9.8 = 0.495 s
Therefore the travel time is 2*0.0495 = 0.99 s

Answers:
(a) 4.85 m/s
(b) 0.99 s