Drop an apple on the moon and on earth...which is faster?

If you drop an apple from a height of 500 meters on Earth and on the Moon, it will fall faster on the Moon because it keeps accelerating. Could someone please show the math for proving this, assuming that the apple reaches a terminal velocity of 42 m/s, Earth's gravity=10m/s/s and Moon's gravity=1.7m/s/s. It would be preferred if you could use relatively simple equations like v=at, d=at^2/2, etc.Drop an apple on the moon and on earth...which is faster?
The correct formula to use is one of the simple equations of uniform linear motion.





v虏 = u虏 + 2as





u = initial velocity = 0


a = acceleration = 1.7 m/s虏


s = height = 500





When rearranged





v = sqrt(2as) = 41.2 m/s on the moon





The apple on earth will approach terminal velocity asymptotically due to air resistance. To prove the apple reached a faster velocity from this height on the moon is difficult without doing calculations involving air resistance. For a height higher than 500m it is trivial. The apple on the moon will reach a higher velocity before impact, whereas the apple on earth will still be limited to falling at its terminal velocity of 42m/s.Drop an apple on the moon and on earth...which is faster?
~4 seconds to reach 42 m/s. ~40 meter (then takes 11sec to hit the ground. 15 sec total





s = 1/2gt^2 sqrt(500*2/1.7) = t = 24.25s.


v = gt=1.7*(24.25) = 41.2m/s





42/1.7; = 24.706sec. to obtain 42m/s on the Moon





(1/2) * (1.7)*(24.70588)^2; =518.823 m to reach 42m/s





{I did the calculations on Maple more carefully}


Anything higher than 518.9m the apple is faster on the moon. It hits the ground faster on the Earth.
Actually, since the Moon's gravity is only 1/6 of Earth's, the acceleration (and, hence, the velocity) will only increase on the Moon at 1/6 of Earth.
v=u + at


0 = 42 + -1.7(t)


-1.7(t) = -42


t = -42/-1.7





But it will fall faster when its on Earth because the acceleration due to gravity is greater than that of the moon......i think...or iam missing sumthing.
If u take the terminal velocity of apple at earth surface=42m/s, then it reaches faster at earth.








the final velocity {velocity at the time of impact} at moon=


v= sqrt (u^2+2as)


=sqrt (0^2+2*1.7*500)= 41.23 m/s





this is less than the terminal velocity of the apple at earth.So the apple at earth reach fast. how ever it is difficult to find the acceleration of an object at earth atmosphere.
The apple dropped on earth is faster due to better gravity. The gravity of earth is six times that of moon.