Two masses m amd 2m approach each other along a part right angles to eachother. After collision, they stick together and move off at 2m/s at an angle 37¤ to the original direction of m....what is the initial speeds of the particles???

Answer 1

initial x momentum = m u
initial y momentum = 2 m v

final x momentum = 3 m (2) cos 37
final y momentum = 3 m (2) sin 37

so
u = 6 cos 37
v = 3 sin 37

Answer 2

add up the momentum vectors. Assuming the particles are moving in the +x and +y directions before the collision, with speeds u and v,

<mu,0> + <0,2mv> = <3m*2sin37°,3m*2cos37°>

now just solve for u and v.