posted by Emily .
If a person can jump a maximum horizontal distance (by using a 45° projection angle) of 2.07 m on Earth, what would be his maximum range on the Moon, where the free-fall acceleration is g/6 and g = 9.80 m/s2?
The classical mechanics equation for distance traveled by a projectile, launched at speed v, angle θ, and height above the ground h, is:
d = v cos(θ) (v sin(θ)+√(v^2 sin^2(θ)+2 g h))/g
When h = 0 and θ=π/4 this reduces to simply:
d = v^2/g
Thus maximum distance is inversely proportional to gravitational acceleration. For the same initial velocity and launch angle, the distance on the moon is then: 6 * 2.07[m].