Question

A vessel at rest at the origin of an xy coordinate system explodes into three pieces. Just after the explosion, one piece, of mass m, moves with velocity (-32 m/s) i Overscript ̂ EndScripts and a second piece, also of mass m, moves with velocity (-32 m/s) j Overscript ̂ EndScripts. The third piece has mass 3m. Just after the explosion, what are the (a) magnitude and (b) direction (as an angle relative to the +x axis) of the velocity of the third piece?

Answer 1

conservation of linear momentum

m1 = m; v1 = -32 m/s i

m2 = m; v2 = -32 m/s j

m3 = 3m = v3 = ??

mvo = m1v1 + m2v2 + m3v3

initaally vessel at rest

0 = m(-32 i ) + m(-32 j) + 3mv3

v3 = 32/3 i + 32/3 j

magnitude

|V3| = sqrt(vx^2+ vy^2)

|V3| = 15.085 m/s

direction = 45 degree counterclockwise from +x direction