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 (-30 m/s)i and a second piece, also of mass m, moves with velocity (-30 m/s)j. The third piece has mass 3m.
(a) Just after the explosion, what is the magnitude of the velocity of the third piece?
(b) What is its direction at this time?
° (counterclockwise from the +x axis)

The momentums have to add to zero.

ah ok thanks?

from what i understand when I solved this problem is that the masses cancel out each other anyway by the end, so just ignore them. Because the two velocities that they give you are vertical and horizontal components square them both and add them and take the square root. Divide by 3 because the third piece is 3m.

(-31)i+ (-31)j+3v=0

To get the direction draw a triangle with the vertical line being 30 and the horizontal line being 30 since they are the horizontal and vertical components of the velocity. Then use tan-1 (30/30) to find the angle.

woops, i put -31 for the equation, i meant to put -30.
oh and the momentums have to add to zero because of the conservation of linear momentum. The initial momentum is 0 since the velocity is 0.