    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 at an angle α to the horizontal with an initial speed of 50 m/s from a point at a distance of 100 m from A as shown in the figure. If the particles collide in the air, find the angle of projection α of particle B. A
30
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B
60
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C
sin 1(35)
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D
cos 1(35)
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Solution

## The correct option is C sin −1(35) Taking x and y−directions as shown in figure, Here, −→aA=−g^j and −→aB=−g^j uAx=60cos30∘=30√3 m/s uAy=60sin30∘=30 m/s uBx=−50cosα and uBy=50sinα 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 line AB. This is posible only when, uAy=uBy (i.e. component of relative velocity along y−axis must be zero) ⟹60sin30∘=50sinα ⟹α=sin−1(35)  Suggest Corrections  0    Join BYJU'S Learning Program
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