    Question

# A particle A is projected with an initial velocity of 60 m/s at an angle 30∘ to the horizontal. At the same time a second particle B is projected in opposite direction with initial speed of 50 m/s from a point at a distance of 100 m from A. If the particles collide in air find the angle of projection α for particle B A
30
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B
37
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C
53
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D
60
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Solution

## The correct option is B 37∘Here, aA=−g^j aB=−g^j uAx=60cos30∘=30√3 m/s uAy=60sin30∘=30 m/s uBx=−50cosα and uBy=50sinα ⇒uAB=(uAx−uBx)^i+(uAy−uBy)^j ⇒uAB=(30√3+50cosα)^i+(30−50sinα)^j Relative acceleration between the two is zero as aA=aB. Hence, the relative motion between the two is uniform. It can be assumed that B is at rest and A is moving with uAB. Hence, the two particles will collide, if uAB is along AB. This is possible only when uAy=uBy i.e. component of relative velocity along y− axis should be zero. or 30=50sinα ∴α=sin−1(35)=37∘  Suggest Corrections  6    Join BYJU'S Learning Program
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