Answer:
18 m, 7.9 m
Explanation:
In the y direction:
y = y₀ + v₀ᵧ t + ½ aᵧ t²
0 = 0 + (v₀ sin 45°) t + ½ (-g) t²
0 = t (v₀ sin 45° - ½ g t)
t = 0, t = 2v₀ sin 45° / g
In the x direction:
x = x₀ + v₀ t + ½ at²
x = 0 + (v₀ cos 45°) t + ½ (0) t²
x = v₀ cos 45° t
Substituting for t:
x = v₀ cos 45° (2v₀ sin 45° / g)
x = v₀² / g
When g = 9.80 m/s², x = 3.0 m:
3.0 = v₀² / 9.80
v₀² = 29.4
On the moon, when g = 9.80/6:
x = 29.4 / (9.80 / 6)
x = 18 m
As you can see, x is inversely proportional to g, so 1/6 the gravity means 6 times the distance. So on Mars:
x = 3 / 0.38
x = 7.9 m
