How far the peg is driven into the ground due to impact?

[Gughanath]

a wooden peg is hit vertically by a mallet which is also moving vertically. The mass of the peck is 0.4kg and the mallet is 2kg. The speed at which the peg starts to move into the ground is 6.67m/s. Given that the ground opposes the motion of the peck with a force of 1kN, find how far the peg is driven into the ground due to impact? Please help me on this one??

 

[Erienion]

Think of it as a mass of 2.4 Kg traveling at 6.67m/s, decelerating at a rate which you can derive from F=ma as it drives into the ground. Calculate the distance for the object to stop.

If you calculate the acelleration the force of the ground gives, you can ask a simpler question by working backwards a bit ; At a=2.77917 ms-2 what distance is traveled to reach 6.67 m/s

:edit to clarify post:

 

[Kelju Ivan]

Wouldn't it be simple to use kinetic energy. The peck has some kinetic energy and the ground does negative work to the peck with a force of 1kN. Just find when the kinetic energy equals the work done by the ground.