A long jump is a clear example of turning sprint speed into distance. The athlete builds horizontal velocity during the run-up, then uses the takeoff foot to redirect part of that motion upward. The jump distance depends on speed, takeoff angle, body position, and how the jumper lands.
This makes the event a powerful real-world model of forces, momentum, and projectile motion.
Key Facts
- Horizontal momentum before takeoff is p = mv, where m is mass and v is velocity.
- The takeoff impulse changes velocity: J = FΔt = Δp.
- Projectile range for equal launch and landing height is R = v^2 sin(2θ) / g.
- For long jump, the best takeoff angle is usually about 18° to 25°, not 45°, because horizontal speed must be preserved.
- Vertical launch velocity controls flight time: t ≈ 2v_y / g for equal launch and landing height.
- Horizontal distance during flight is x = v_x t, so distance increases when horizontal speed and flight time increase.
Vocabulary
- Run-up speed
- Run-up speed is the horizontal speed a jumper builds before reaching the takeoff board.
- Takeoff angle
- Takeoff angle is the angle of the jumper's velocity above the horizontal at the instant the foot leaves the ground.
- Impulse
- Impulse is the product of force and contact time, and it equals the change in momentum.
- Projectile motion
- Projectile motion is the curved motion of an object moving under gravity after it is launched.
- Center of mass
- The center of mass is the average position of an athlete's mass and follows a smooth projectile path during flight.
Common Mistakes to Avoid
- Using 45° as the best long jump angle, which is wrong because real jumpers cannot keep their sprint speed if they launch that steeply.
- Ignoring horizontal velocity, which is wrong because most long jump distance comes from carrying sprint speed through takeoff.
- Treating the athlete's arms and legs as changing the flight path of the center of mass, which is wrong because body motions mainly change rotation and landing position after takeoff.
- Forgetting that takeoff takes time, which is wrong because the ground force during foot contact creates the impulse that redirects motion upward.
Practice Questions
- 1 A jumper leaves the board with a horizontal velocity of 9.2 m/s and stays in the air for 0.72 s. How far does the center of mass travel horizontally during flight?
- 2 A 65 kg jumper has a horizontal speed of 9.0 m/s before takeoff. What is the jumper's horizontal momentum?
- 3 Two jumpers have the same flight time, but one has a greater horizontal velocity at takeoff. Explain which jumper should travel farther and why.