Michael Jordan holds the record for the highest vertical jump in NBA history. He could jump 48 inches vertically (for example, Kobe Bryant has a 38-inch leap, Dwight Howard has a 39.5-inch leap, and LeBron James has a 44-inch leap). How much time did Jordan spend in the top 6 inches of the jump and how much time in the bottom 6 inches of the jump? In your own words, explain why basketball players seem to be suspended in the air when they jump? a(t) = -g (gravity) = -32 ft/s V(t) = -32t + Vo: Vo = initial velocity (depends on the player) s(t) = -16t^2 + Vo t + So: So = 0 (jumps from ground level)
The Correct Answer and Explanation is:
Let’s break this down using the given equations of motion.
Michael Jordan’s jump height is 48 inches (or 4 feet). His motion follows:
- Acceleration: a(t)=−32a(t) = -32 ft/s² (gravity acting downward)
- Velocity: V(t)=−32t+VoV(t) = -32t + V_o
- Position: s(t)=−16t2+Vots(t) = -16t^2 + V_o t
To determine how much time he spends at different heights:
- Finding initial velocity VoV_o at the start of the jump At the peak (V=0V = 0):
0=−32t+Vo0 = -32t + V_o
Solving for tt, we use s=4s = 4 feet and set VoV_o based on reaching that height:
4=−16t2+Vot4 = -16t^2 + V_o t
After solving, we get Vo=163V_o = 16 \sqrt{3} ft/s and total time to reach the peak is tpeak=Vo32=32t_{\text{peak}} = \frac{V_o}{32} = \frac{\sqrt{3}}{2} seconds ≈ 0.866 seconds.
- Time spent in the top 6 inches The top 6 inches are between 3.5 feet and 4 feet of the jump. Using kinematics, we find he spends around 0.07 seconds in this range.
- Time spent in the bottom 6 inches The bottom 6 inches are between 0 and 0.5 feet. He moves through this range very fast—around 0.02 seconds.
Why Players Seem to Hang in the Air
The perception that basketball players “float” in the air is due to the physics of motion and human perception. The jump follows a parabolic trajectory, meaning players spend more time near the peak compared to when they are near the ground. This happens because:
- Deceleration near the peak As the player rises, gravity gradually slows them down. Near the highest point, their velocity is very low, making their motion appear slow. This makes it seem like they are “hanging” mid-air.
- Rapid acceleration at takeoff and landing Near the ground, players accelerate rapidly, covering the first few inches much faster than the last few inches. Since movement is fast at launch and landing, we notice those phases less, while the top phase stands out.
- Human perception bias Our brains pay more attention to slower motion rather than high-speed movement. The gradual slowdown at the peak creates an illusion that the player is “floating” longer, even though the total jump follows normal physics.
Jordan’s legendary hang time wasn’t just about skill—it was also the magic of physics working in his favor!
