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Question

A particle of mass m is projected from the ground with an initial speed u0at an angle αwith 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
Velocity of the particle performing projectile motion at highest point
=V1=V0cosα
Velocity particle thrown vertically upwards at the position of collision

=v22=u202gu2sin2α2g=v0cosα

So, from conservation of momentum

tanθ=mv0cosαmu0cosα=1

θ =π/4

102424_31868_ans.PNG

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