A ball of mass 1kg is thrown vertically upwards from a building with a speed of 10m/s, and another ball of mass 3kg is dropped from the same point towards the ground with the same speed. At what time will the centre of mass have the maximum height w.r.t the ground? Assume balls are left at t=0.

When the balls are released in their respective directions, the ball going downwards is heavier and is covering more distance per unit time. This is because both the balls have the same initial speed and the heavier ball is gaining speed downwards while the other ball is losing speed as it moves upwards. Their mid-point will be below the point of release and centre of mass, will therefore, be even below that point, since heavier mass is moving downwards.