Abody 'a' of mass 1.5kg travelling along the positive x-axis with speed of 4.5m/s collides with another body 'b' of mass 3.2kg, which initially is at rest as a result of the collision, 'a' is deflected and moves in a speed of 2.1m/s in a direction which is at an angle of 30 degree below the x-axis. 'b' is set in motion at an angle φ above the x-axis. calculate the velocity of 'b' after the collision.

We can solve this problem using only the law of conversion of energy. Because you don't need to calculate the angle you don't have to deal with momentum and this makes this problem a lot easier. A good portion of the information about the problem is redundant. We have masses of both bodies and velocity of body A before and after the collision. You can see that it's velocity decreased, that's because some of it's initial energy was transferred to body B. 
Let us write down the law of conversion of energy.



The final answer is: 

Amethod of procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses.

Ihope you find the answer