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Question

A particle of mass m is projected from the ground with an initial speed u0 at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u0. The angle that the composite system makes with the horizontal immediately after the collision is ?


A

π4

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B

π4+α

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C

π4α

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D

π2

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Solution

The correct option is A

π4


At the instant of collision, momentum of the first particle =mu0 cos α [Horizontal]
Velocity of second particle at collision =u202gu20sin2α2g=u0 cos α
Momentum of the second particle =mu0 cos α [Vertical]
Now, tan θ=mu0 cos αmu0 cos α=1θ=45


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