Rotation of Earth and falling objects

[ViolentCorpse]

Hello everyone!

If a ball is released from the top of a very tall building, would it land ahead in the direction Earth is rotating (to the east) or would it lag behind i.e the Earth "moves out" from underneath it so it lands to the west? I think it should land ahead to the east since its tangential velocity is greater than that of the ground, but I'm not sure.

Thank you very much!

 

[jbriggs444]

Yes, all things being equal, it would land to the east. As you point out, the top of the building is moving slightly faster eastward than the bottom and ball continues to carry this excess as it falls.

Back of the envelope...

For a 100 meter building the fall will nominally take 5 seconds (neglecting air resistance). The Earth is rotating at 2pi radians in just under 24 hours. With a 100 meter delta in radius, that's about 7 millimeters per second. Over a 5 second fall that would amount to about 3.5 centimeters.

 

[sophiecentaur]

AKA Coriolis Force.

 

[ViolentCorpse]

Thanks both of you! Appreciate it. :)