physics hw help?

Question

Two objects, one moving north, one moving east, collide and stick together. If the eastbound object has three times the mass of and is initially moving half as fast as the northbound object, which of the indicated paths represents the most likely final motion of the pair? Justify your answer using the concept of linear momentum.

Answer 1

The center of mass will retain momentum and direction

Northbound has mass m and speed 2*v
Eastbound has mass 3*m and speed v

The combined mass is 4*m and the momentums are
4*m*vy=2*m*v

vy=v/2

4*m*vx=3*m*v
vx=3*v/4

The magnitude of the speed after collision is
=v*sqrt(9/16 + 1/4)

and the direction is
tan(th)=2/3 North of East

j

Answer 2

Where are the indicated paths?

Let 3m be the mass of object moving east with velocity v and m be the mass of object moving north with velocity 2v. After collision they stick together and the combined mass 4m has velocity u (vector).

By law of conservation of momentum,

3mv i + 2mv j = 4m u (vector)
=> u (vector) = (3/4 i + 1/2 j) v

Hence it moves in a direction north of east = arctan [(1/2)/(3/4)]
=north of east (71.6°)