Find the magnitude f of the force that the wooden block exerts on the nail, assuming that this force is independent of the depth of penetration of the nail into the wood. you may also assume that v0≫2gl−−−√, so that the change in the hammer's gravitational potential energy, as it drives the nail into the block, is insignificant. express the magnitude of the force

The answer would be (M * v_0^2) / (2L) 

The reason behind this is explained by the work theorem:

Kf – Ki = -.5Mv_0^2 
W = -FL 
Kf – Ki = W consulting to work energy theorem. This specifies that the alteration in the kinetic energy of a particle is equivalent to the whole work done on that particle through all the forces that act on it. 
To make things easier to find that F = (M*v_0^2)/2L 

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards