Projectile Motion: Comparison of Maximum Altitudes on Earth and Moon

[changzv]

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.

How does the maximum altitude of the projectile on the Moon compare with that of the projectile on the Earth?


Both initial velocity on the Moon and Earth is the same.
I know that gravity of the moon is 1/6th the gravity of the Earth.
So is the maximum altitude of the projectile on the Moon 6 times greater than the projectile on the Earth? Is there something I'm missing out on?

 

[zachzach]

Yes, you are missing something. You are only using your intuition and not actual laws of physics. Try to prove your statement mathematically. Use equations of motion when the acceleration is constant (which is very close to being true when the projectile does not go too high).

 

[changzv]

I tried using v^2 = u^2 +2as.
Initial velocity = 0, so u^2 = 0
v^2 = 2as when a = 9.81, s= v^2/19.62
v^2 = 2as when a = 1.635, s=v^2/3.27

What value of v can I use? Or am I using the wrong formula?

 

[zachzach]

The initial velocity is zero? If that was true the projectile would not go anywhere. You wrote: 'A projectile is launched on the Earth with a certain initial velocity'. Also, think about what the velocity is at the maximum height.

 

[changzv]

I see! I didn't read the question carefully sorry.
Velocity at maximum height is 0, so v=0.
And the Initial velocity on the Moon and the Earth is the same.
Simultaneous equation?
v^2=u^2+2as
u^2=-2as, u^2 for Earth and Moon is the same.
-2as(Earth) = -2as(Moon)
s(Moon)/s(Earth) = 19.62/3.27
= 6
Did i go wrong somewhere?

 

[zachzach]

That's what I got. Your tuition ended up being right.

 

[changzv]

Thanks for clarifying!