The distance a person can jump on different planets of varying gravity?

Question

If a person can jump a maximum horizontal distance (By using a 45 degree projection angle) of 3.0m on the Earth, what would be his maximum range on the Moon, where the free-fall acceleration is g/6 and g=9.8m/s^2? Repeat for Mars, where the acceleration due to gravity is 0.38g.

The answers are:
18m on the moon; 7.9m on Mars.

How do I arrive at those answers?

Answer 1

his initial velocity v0 = sqrt(range*g/sin(2theta)) = 5.422 m/s.
v0[x] = v0*cos(theta), v0[y] = v0*sin(theta)
The equations to find range are:
time of flight t = 2*v0[y]/a
range = v0[x]t = 2v0[x]*v0[y]/a
So range is inversely proportional to a.
When a=g, range = 3 m.
When a=g/6, range = 18 m.
When a=0.38g, range = 7.8947 m.