ClassX Video Lessons The math behind Michael Jordan’s legendary hang time – Andy Peterson and Zack Patterson
Michael Jordan, the legendary basketball player, once remarked, “I don’t know whether I’ll fly or not. I know that when I’m in the air sometimes I feel like I don’t ever have to come down.” However, thanks to Isaac Newton’s laws of physics, we understand that what ascends must eventually descend. This principle applies even to Jordan, whose famous dunk from the free-throw line has been calculated to last just 0.92 seconds.
The concept of hang time, or the duration from when one’s feet leave the ground to when they return, is limited by Earth’s gravity. On a flat surface, this time is typically around one second. Gravity exerts a force that pulls all objects toward the Earth’s surface at an acceleration of 9.8 meters per second squared. The moment you jump, gravity begins its work to bring you back down.
Using our understanding of gravity, we can derive a straightforward equation to model hang time. This equation calculates the height of a falling object above a surface as a function of its initial height, initial velocity, time spent in the air, and gravitational acceleration. When applied to Michael Jordan’s free-throw dunk, where he starts at ground level with an initial vertical velocity of 4.51 meters per second, the equation reveals a parabolic trajectory.
The parabola’s vertex indicates Jordan’s maximum height of 1.038 meters, while the X-intercepts show the moments of takeoff and landing, with the difference representing the hang time. Earth’s gravity makes it challenging for even the most skilled athletes to achieve significant hang time.
Imagine if Michael Jordan played an away game on another celestial body. On Venus, where gravitational acceleration is 8.87 meters per second squared, similar to Earth’s, Jordan could achieve a hang time slightly over one second, reaching more than a meter off the ground. In contrast, Jupiter’s intense gravitational pull of 24.92 meters per second squared would limit his jump to less than half a meter, with a hang time of just 0.41 seconds.
The moon, however, presents a different scenario. With its weaker gravity, Jordan could leap from behind half-court, soaring over six meters high, and enjoy a hang time exceeding five and a half seconds. Such a feat would indeed make it seem as though he could fly.
While Earth’s gravity imposes limits on hang time, exploring the physics behind it offers fascinating insights into how different gravitational forces affect our ability to stay airborne. Whether on Earth or elsewhere in the solar system, the interplay between gravity and motion continues to captivate our imagination.
Using a stopwatch, measure the time from when you jump to when you land. Record your hang time and compare it with Michael Jordan’s 0.92 seconds. Discuss how close you are to his hang time and what factors might affect your results.
Plot the trajectory of a jump using the equation for height as a function of time. Create a graph showing the parabolic path of your jump. Compare your graph to the one described for Michael Jordan’s jump and discuss the similarities and differences.
Use a simulation tool to model how different gravitational forces affect hang time. Try simulating jumps on Earth, the Moon, and Jupiter. Record your observations and discuss how gravity influences the height and duration of your jumps.
Research the gravitational forces on different planets and moons in our solar system. Calculate the potential hang time for a jump on each celestial body. Create a chart to display your findings and present it to the class.
Engage in a class discussion about how physics, particularly gravity, affects various sports. Consider sports like basketball, soccer, and gymnastics. Share your thoughts on how understanding physics can improve athletic performance.
Gravity – The force that pulls objects toward each other, especially the force that pulls objects toward the Earth. – The apple fell from the tree because of gravity pulling it down to the ground.
Hang Time – The total time an object spends in the air after being thrown or jumped. – The basketball player’s hang time was impressive as he soared above the rim before making the dunk.
Physics – The branch of science that studies matter, energy, and the forces that act on them. – In physics class, we learned how different forces affect the motion of objects.
Jump – To push oneself off the ground and into the air using the legs. – When I jump off the diving board, I feel like I’m flying for a moment.
Velocity – The speed of an object in a specific direction. – The car’s velocity increased as it went downhill, making it go faster.
Height – The measurement of how tall something is from the base to the top. – The height of the roller coaster made me feel a little nervous before the drop.
Surface – The outermost layer or boundary of an object or area. – The surface of the water was calm and smooth, reflecting the sky above.
Acceleration – The rate at which an object changes its velocity. – The car’s acceleration was quick when the driver pressed the gas pedal.
Trajectory – The path that an object follows as it moves through space. – The trajectory of the basketball was perfect as it swished through the net.
Moon – The natural satellite that orbits the Earth and is visible at night. – We learned about the moon’s phases in science class and how they change throughout the month.
