Answer to Question #228207 in Physics for Ekott jnr

Question

Two Masses, m and 2m, approach each other along a path at right angles to each other . After collision, they stick together and move off at 2m/s at angle 37⁰ to the original direction of the mass m. What were the initial speeds of the two particles ??

Answer 1

Let us denote initial velocities of the masses as $v_1$ and $v_2$. The law of conservation of a momentum gives:

$$m{\bf v_1}+2m{\bf v_2}=(m+2m)\bf u$$

In projection:

$$mv_1=3mu\cos 37^{\circ}\\ 2mv_2=3mu\sin 37^{\circ}$$

Hence,

$$v_1=3*2\:{\rm m /s}\cos37^{\circ}=4.8\:{\rm m/s}\\ v_2=3/2*2\:{\rm m /s}\sin37^{\circ}=1.8\:{\rm m/s}$$