Help is greatly appreicated on this problem. Thank you A triangular wedge 6 m hi

Question

Help is greatly appreicated on this problem. Thank you

A triangular wedge 6 m high, 13 m base length, and with a 13 kg mass is placed on a frictionless table. A small block with a 5 kg mass ( and negligible size ) is placed on top of the wedge as shown in the figure below. All surfaces are frictionless, so the block slides down the wedge while the wedge slides sidewise on the table. By the time the block slides all the way down to the bottom of the wedge, how far delta Xwedge does the wedge slide to the right? Answer in units of m

Explanation / Answer

Just applying law of consevation of momentum solves our problem
mu1+Mv1=(m+M)V+mu2
m*0+M*0=(m+M)V+mu2
V=-mu2/(m+M)

Xwedge/t =-5*(L/t)/(5+13)

      Xwedge=(-5/18)*(6^2+13^2)

                      =-3.9772m

wedge move by 3.9772m opposite to direction of block motion.

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