A vessel at rest at the origin of an xy coordinatesystem explodes into three pie

Question

A vessel at rest at the origin of an xy coordinatesystem explodes into three pieces. Just after the explosion, onepiece, of mass m, moves with velocity v in thenegative x direction, and a second piece, also of massm, moves with the same velocity in the negative ydirection. The third piece has mass 3m. Just after theexplosion, (a) what is the magnitude of thevelocity of the third piece in terms of the given variables?(b) What is the direction of its motion (as anangle relative to the positive x axis)?

(a)

Explanation / Answer

initial momentum = 0 on both x and y direction so thefinal should be zero too. in x direction we have => -v*m +3m*vx = 0 so xcompoent of the vel of third one is vx = v/3 similarly for y direction => -v*m +3m*vy =0     so vy= v/3 again positivedirection. total velocity magnitude is v= (vx^2 +vy^2) =v2/3 = 0.47 v b) direction find angle tan = vy/vx = 1 so = + 45 degrees abovex axis enjoy it

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