A particle of mass $$10 \mathrm{~kg}$$ moving eastwards with a speed $$10 \mathrm{~m} / \mathrm{s}$$ collides with another particle of the same mass moving northward with the same speed $$10 \mathrm{~m} / \mathrm{s}$$. The two particles coalesce on collision. The new particle of mass $$20 \mathrm{~kg}$$ will move in the north-east direction with velocity.

A projectile is launched vertically from the earth with speed $$v_1$$ hits a satellite at the height $$h$$ moving with speed $$v_2$$. If both have the same mass $$m$$, then what is the common velocity if they move together after the collision?