A14 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.

The momentum change of the rock caused by its fall will be m/sec and the magnitude of the earth velocity will be 140 kgm/s

When the rock starts from rest and free falls through a certain distance causes a change in the momentum of the rock.

Given,

Mass of the rock = 14 kg

Distance traveled by the rock under the influence of gravity =5.0m

Mass of earth =

Assumptions: the rock earth system is closed.

To find  

The momentum change of the rock    

Megnitude of earth velocity

 If the body freely falls initial velocity will be zero.

 so ; u = initial velocity = 0

  a= acceleration due to gravity ; g =10 m/s^2

  t= 1 second

Change in the momentum of the rock will be,

ΔP= FΔT

As we know F= mg

ΔP = (mg ) ΔT

ΔP= (14)

 ΔP=140 kg-m/s²

The change in the momentum of the rock is 140kg-m/s²

As we know that change in the momentum has conserved

change in the momentum of earth = change in the momentum of the  rock

ΔV

ΔV =m /sec

The change in the megnitude of the earth velocicty  is   m /sec .

To know more about the change in momentum refers to

link

mass of the rock = 14 kg

distance that rock will move down = 5.0 m

now for motion under gravity we know that

here we have

by solving above equation we have

now change in momentum of rock is related to the force on it by equation below

Now we know that same amount of force will act on the Earth also

So Earth will also have same momentum change

now we have

it becomes positively charged by charging it