Asap and show ! a 14 kg rock starting from rest free falls through a distance of 5.0 m with no air resistance. find the momentum change of the rock caused by its fall and the resulting change in the magnitude of earths velocity. earth mass is 6.0 * 10^24 kg. show your work assuming the rock earth system is closed.

Time taken to fall the rock from rest

here we know that

now we have

Now we know that

here Force (F) is due to gravity

so we have

now we can plug in all data

So change in momentum of rock will be 140 kg m/s

Now we know from Newton's III law

so we have

now we have

so above is the speed of Earth

whichever one it is, it's definitely not one that you included on the list you provided.