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Q.

It is possible to project a particle with a given velocity in two possible ways so as to make it pass through a point at a distance r from the point of projection. The product of times taken to reach this point in the two possible ways is then proportional to

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a

r

b

r2

c

1/r

d

1/r2

answer is A.

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Detailed Solution

The range of projectiler=u2sin⁡2θg=2u2sin⁡θcos⁡θgThe two possible angles of projection are θ and 90∘−θ. The times of flight corresponding to these angles aret1=2usin⁡θgand    t2=2usin⁡90∘−θg=2ucos⁡θg∴ t1t2=4u2sin⁡θcos⁡θg2=2rg or  t1t2∝r
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