See the following case;
A stone of mass 5 kg falls from a 50 metre height and buries 1 meter deep in the sand.find the average resistance offered by sand and the time it takes to penetrate

You can use energy principles to find the force F. The PE of the mass 50 meters in the air is give by PE = mgh. When the stone drops to the ground that PE is converted to KE. And for the sand to stop the stone the work done is Fd, which equals the KE. You have values for m, g, h and d, so solve for F.

For the time it takes to penetrate there are a couple of ways to approach it:

1. Calculate the velocity with which the stone hits the sand, and then use and solve for .

2. Calculate the acceleration of the stone in the sand from F=ma, and then find t from .