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Question

A body is projected at 30 with velocity v1 from point A on the ground. At the same time, another body is projected vertically upwards from B with velocity v2 from the ground. The point B lies vertically below the highest point of the trajectory of ball A. For both the bodies to collide, what should be the ratio of v1v2 ?

A
1
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B
2
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C
12
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D
2
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Solution

The correct option is D 2
For balls to collide, vertical height covered by ball A must be equal to the vertical height covered by ball B in same time.
Let T be the time of flight of the projectile for ball A.
Let H be the maximum height of the projectile of ball A.
Time taken by ball A to reach maximum height of the projectile =T2
For Ball A:
H=v1sin30(T2)12g(T2)2 ....(i)
(Using second equation of motion)
For Ball B:
H=v2(T2)12g(T2)2....(ii)
On comparing (i) and (ii), we get
v12=v2v1v2=2

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