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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A particle is projected vertically upward with velocity u from a point A , when it returns to the point of projection .

A particle is projected vertically upward with velocity u from a point A , when it returns to the point of projection .

A particle A is projected with speed V_(A) from a point making an angle 60^(@) with the horizontal. At the same instant, a second particle B is thrown vertically upwards from a point directly below the maximum height point of parabolic path of A, with velocity V_(B) . If the two particles collide then the ratio of V_(A)//V_(B) should be:

A particle A is projected with speed v_(A) from a point making an angle 60^(@) with the horizontal. At the same instant, a second particle B is thrown vertically upwards from a point directly below the maximum hieght point of parabolic path of A with velocity v_(B) . If the two particles collide then the ratio of v_(A)//v_(B) should be

A particle A is projected with speed v_(A) from a point making an angle 60^(@) with the horizontal. At the same instant, a second particle B is thrown vertically upwards from a point directly below the maximum hieght point of parabolic path of A with velocity v_(B) . If the two particles collide then the ratio of v_(A)//v_(B) should be

A particle A is projected with speed V_(A) from a point making an angle 60^(@) with the horizontal. At the same instant, a second particle B is thrown vertically upwards from a point directly below the maximum height point of parabolic path of A, with velocity V_(B) . If the two particles collide then the ratio of V_(A)//V_(B) should be: