A particle `P` is projected with velocity `u_1` at an angle of `30^@` with the horizontal. Another particle `Q` is thrown vertically upwards with velocity `u_2` from a point vertically below the highest point of path of `P`. Determine the necessary condition for the two particles to collide at the highest point.
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Explanation

Both particles collide at the highest point. It means the vertical distance travelled by both the particle will be equal, i.e., the vertical component of velocity of both particle will be equal
`u_1 sin 30^@ = u_2 rArr (u_1)/(2) = u_2 rArr u_1 = 2 u_2`.