1) a cannon fires a shell that explodes that eplodes into two identical fragment

Question

1) a cannon fires a shell that explodes that eplodes into two identical fragments at the higest point of its trajectory, a distance L from the cannon.  One of the fragments retraces its trajectory back and returns to the cannon.  One of the fragments retraces its tragectory back and returns to the cannon.  Where will the second fragment land?

answer = 4L

2) a metal pole of length L and mass M is lying on the ground.  What is the least amount of work needed to put it in the upright position?

answer = mgL/2

3) Two objects collided while moving along the same straight line and exchange their velocites.  After the collision, both objects continue moving along the same straight line.  What is the ratio of the masses of these objects? Was the colision elastic?

answer = 1, yes

I have the answers to these problems im interested in the solutions, thanks!

Explanation / Answer

1)it is fragmented at half its range(=2L)

Since no external force is exerted Centre of mass should lie at the point where it actually be falling i.e at 2L

Thus taking starting point as origin we have

Centre of mass = m/2 *x /m = 2L

Thus x=4L

2)Treating the pole at its centre of mass .

Centre of mass should travel a distance of L/2 for making it upright

Thus change in its centre of mass potential energy is the minimum energy to be supplied = m*g*L/2

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