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Question

Two projectiles each of mass m are projected with same velocity v making an angle α and β from the same point in opposite directions. Find the change in their momentum at any instant :

A
2mvsin(α+β)
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B
2mvsinα+β2
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C
2mvcos(α+β)
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D
2mvcosα+β2
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Solution

The correct option is D 2mvcosα+β2
Horizontal change in momentum Δpx=m[vcosα(vcosβ)]

Vertical change in momentum Δpy=m[vsinαgt(vsinβgt)]

Net change in momentum Δp=Δp2x+Δp2y
=mv(cosα+cosβ)2+(sinαsinβ)2

=mv2+2(cosαcosβsinαsinβ)
=2mvcosα+β2

205229_134664_ans_a3e8d47d388b4a6e90c4c03c6515a1b9.png

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