See the attachment
Once you read the question (attached) you'll notice that there are two different parts of the question, the first one asks to find the combined velocity of the system after collision while the 2nd one uses the result of the first part and states to find the force.
Acceleration due to gravity = g
(for constant acceleration) average velocity= (v+u)/2
Impulse, I = Ft (for a constant force)
The Attempt at a Solution
I solved the first part by finding the velocity of the combined system to be "x"
x = mv/(M+m)
but i am unable to solve the 2nd part of the question.
Here is what i did :
Momentum(initial) = mv
Momentum(final) = x(M+m)
Force (with which the ground resists penetration) = (m+M)x/t
As the force is constant thus the acceleration would also be constant, thus :
average velocity = [v(initial) +v(final)]/2
v(initial) = v one the other hand v(final) = 0 [because the system comes to rest]
thus average velocity = v/2
by solving for "t" and then substituting "t" in the Force(with which the ground resists penetration) equation we get the final result of the force.
Further Comments :
The result found by my method is wrong, instead the solution to this question involves the use of Weight of the combined system which is downward thus acting opposite to the Force(with which the ground resists penetration).
How can we take "Weight = (M+m)g" into account in this question, how do i include "g" in my answer to make it match with the correct solution ?