Physics Of Basketball — Hang Time
The figure below shows the typical trajectory a basketball player might travel as he makes a jump.
You can visually see that almost half the hang time is spent near the top of the arc.
d is the vertical jump distance
V1 is the vertical component of jump velocity at take-off
t is time
g is the acceleration due to gravity, which is 9.8 m/s2
Maximum jump height is reached at t = V1/g.
Using the above formula for d, the maximum height reached is
dmax = (V1)2/(2g).
Now, set t = V1/(2g), this is half the time it takes to reach maximum height. Call this time thalf.
Using the above formula for d, the height reached during thalf is
dhalf = 3(V1)2/(8g).
Now, calculate the following ratio:
dhalf/dmax = 0.75
This interesting result tells us that half the hang time is spent in the bottom 75% of the jump. The remaining time is spent in the top of the jump (the top 25% of the jump). In other words, half the jump time is spent in the highest 25% of the jump (the top part of the arc). This explains why a basketball player appears to "hang" during the jump.
So, a player who can jump 4 feet vertically will have a hang time of around a second, with half a second spent in the high part of the jump.
Physics Of Basketball — Backspin
Backspin is used by players to improve their chances of getting the basketball into the net. When an object is spinning and bounces off something, it will have a tendency to bounce in the direction of the spin. This is useful for players who bounce the ball off the backboard, or the back of the net. The resulting bounce will more likely send the ball downwards into the net. Without backspin the ball is more likely to bounce away from the net.