pls help me.. it is possible to project a particle from level ground with a given velocity in 2 possible ways so as to make it pass through a point on the ground at a distance r from the point of projection .The product of time taken to reach this point in the 2 possible ways is then proportional ro a. r b. 1/r

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pls help me.. it is possible to project a particle from level ground with a given velocity in 2 possible ways so as to make it pass through a point on the ground at a distance r from the point of projection .The product of time taken to reach this point in the 2 possible ways is then proportional ro a. r b. 1/r

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The answer is a) r. If the particle is thrown at an angle θ with initial velocity u, then r will be \[r = u ^{2}\sin2\theta/g ^{2}\] Then, the particle can be thrown with two different angles θ and (pi/2 - θ) to pass through the same point at distance r. Now, the time taken for the particle is \[T1 = 2usin \theta/g\] and \[T2 = 2usin(\pi/2 - \theta)/g = 2ucos \theta/g\] Now, (T1xT2) is proportional to r.
i was stuck..thank u 4 helping... :) !

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