A body of mass is dropped from a height h on a sand floor. If the body penetrates X cm in to the sand , the average resistance offered by the sand to the body is:

The body is dropped from a height ‘h’. It hits the floor with velocity say ‘v’.

So, v² = u² + 2gh

=> v² = 2gh

Then it penetrates in to the sand through ‘X’ cm and stops. Again using,

v² = u² + 2as

=> 0 = 2gh + 2aX

=> a = -gh/X

If ‘m’ is the mass of the body then the resistance offered by the sand is = -ma

= -m(-gh/X)

= mgh/X

This is the resistance offered by sand to the body.