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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 ydirections as shown in figure,

Here, aA=g^j and aB=g^j
uAx=60cos30=303 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 yaxis must be zero)
60sin30=50sinα
α=sin1(35)


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