An object of mass 2m is travelling at a speed of 5.0 m s⁻¹ in a straight line. It collides with an object of mass 3m which is initially stationary, as shown in Fig. 3.1.

After the collision, the object of mass 2m moves with velocity v at an angle of 30° to its original direction of motion. The object of mass 3m moves with velocity w also at an angle of 30°, as shown in Fig. 3.2.

By considering the conservation of momentum in two dimensions, calculate the magnitudes of v and w.