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While checking for an elastic collision, we see whether the statement "relative speed of approach was equal to relative speed of separation" is satisfiedView attachment 35948
why is answer A
Now the key term is 'relative'. For two bodies moving in opposite direction to each other, let's say, you are driving at 50 km/h, and there is another car coming towards you at 50 km/h. Thus, the relative speed of the incoming car would be 100km/h, as you are going in the opposite direction.
Now let's say you are overtaking a car which is driving at around 50 km/h, while you are driving at 60 km/h. Your relative speed would thus be 10 km/h only.
Now, let's look at the question. (NOTE: The question is talking about speed, not velocity)
Ux and Uy are moving in opposite directions, thus their speeds are added as we are finding about the relative speed.
Vx and Vy are moving in opposite directions, thus again their speeds are added.