How to find the height where two same marbles have the same velocity?

Question

How do you find the height where two same marbles have the same velocity when one marble is dropped from the Earths atmosphere (g=9.8) and the other is dropped from the Moons atmosphere (g=1.6)? Both are dropped from the same height

I have absolutely no idea where to start...

Answer 1

What you have is the Earth marble accelerating faster but reaching a terminal velocity, and the Moon marble accelerating slower but not limited to a terminal velocity because there's no atmosphere. If the question doesn't specify the drop height you won't be able to calculate the height of equal velocity. (Or maybe the question wants the ground impact speed, and the drop height is the unknown? That would be sufficient.) Once that's defined, calculating the Earth marble's terminal speed requires that you know its density and size, and even then that could be tricky because the air density increases, and thus the terminal speed decreases, with decreasing altitude. So right now your question gives insufficient information, and it's pretty difficult even if you have all the needed data. Sorry about that.