Velocity on the moon?

Question

If identical guns fire identical bullets at the same speed from the same height above level planes, one on the earth and one on the moon, what is true:
1 the horizontal distance travelled by the bullet is greater for the moon.
2 The flight time is less for the bullet on earth
3 The velocities of the bullets at impact are the same

I think 1 and 2 are true but what about 3?
I don't think it's true because if I would calculate V, I would have to use g and for the moon that's 1.63m/s making the result different than the result we would get on earth using 9.8m/s.
Who can explain this to me please?

Answer 1

OK.
By using simple kinematics, once the bullets are fired, there are no more horizontal forces acting upon them if we eliminate atmospheric drag. But, should atmospheric drag (friction) be present, it wouldn't make a difference on our answers of yes and no, but it would make a difference in the quantitative results (which we aren't concerned with). So, no "x" directional forces. Thus the only forces we have to concern ourselves with are the "y" (vertical) forces that are acting upon the bullets, namely gravity.

Newton's 2nd law: F = ma
F = force
m = mass
a = acceleration

On Earth, the force of gravity is: F = mg
where F = force acting upon the bullet
m = mass of the bullet
g = 9.8m/s^2 down

On the moon, the force of gravity is F = ml
where F and m have the same definitions as above but
l = 1.6m/s^2 down.

Now, because there is a less acceleration in the down direction from lunar gravity as there is from terrestrial gravity the bullet will:
1) Go further horizontally
2) fly longer
and
3) hit with less velocity
on the moon than on Earth.

This last one (#3) is a bit tricky, but let's look at it in more detail.

Both bullets must fall the same distance to reach the surface of their respective planets. Note here, that velocity is defined by distance over time, or
v = m/s
for our purposes. Now, when we look at the equation, m (distance to reach the planet surface) will be the same for both bullets, but the time they take to reach that surface is more on the moon than on Earth. Thus v(moon) will be smaller than v(earth). Another way to think about it is it will move the same veritcal distance much faster on the Earth, thus having a greater velocity there, than it will on the moon.

hope this helps

Answer 2

1 and 2 are true but forgetting maths it's easy to work out whether 3 is true using logic... (but there are actually two answers confusingly!)

If you think of gravity as another expression of 'atmosphere' - the atmosphere on earth is greater than that of the moon, so the bullet would hit more particles that would slow it down....
- so the bullet on the moon would be faster at impact if you were firing at a target as it would not have had as many particles slow it down
- but if the word 'impact' means when the bullet hits the ground - then although it would take longer for the moon bullet to have been slowed down (ie: the flight time is longer) the actual velocity of the bullet at impact would be the same for that of the bullet on earth...

Hope that helps!

Answer 3

3 is false for the same reason that 2 is true .. .namely atmospheric drag.