A projectile is launched on the Earth with a certain initial velocity and moves

Question

A projectile is launched on the Earth with a certain initial velocity and moves without air resistance. Another projectile is launched with the same initial velocity on the Moon, where the acceleration due to gravity is 1/6 as large. Part One) How does the range of the projectile on the Moon compare with that of the projectile on the Earth? a) 1/6 as large b)the same c) root of 6 times larger d) 6 times larger e) 36 times larger. Part Two) How does the maximum altitude of the projectile on the Moon compare with that of the projectile on the Earth? Choose from the same possibilities a) through e).

Explanation / Answer

range of object projected at an angle
R = (V²/g)sin(2)
V is initial velocity in m/s
g is the acceleration of gravity 9.8 m/s²
Time of flight = R/(Vcos)
Max height
h = (V²/2g)sin²

Range is inversely proportional to g, as is max height, so (d) 6 times larger  is correct in both cases. Interestingly, for time of flight, g is not a factor.

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