Multiple choice

A boat which is rowed with constant velocity u, starts from point A on the bank of river which flows with a constant velocity v and its points always towards a point B. On the other bank exactly opposite to A, the equation of the path of boat is:

  1. $r\sin \theta =c\left(\tan \dfrac{\theta}{2}\right)^{u/v}$
  2. $r\sin\theta =\dfrac{u}{v}$
  3. $r^2\sin\theta =\dfrac{u}{v}$
  4. $ur^2=v\sin^2\theta$

  5. None of the above
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A Correct answer
Explanation

This is a classic pursuit problem. The path of a boat moving towards a target moving at a constant velocity is described by a specific differential equation, which leads to the solution r * sin(theta) = c * (tan(theta/2))^(u/v).

AI explanation

This scenario describes pursuit navigation where the boat is constantly pointed towards the opposite point B. Applying the standard differential equation for such a pursuit curve in a moving river yields the path traced by polar coordinates. The corresponding equation of the path of the boat is $r\sin \theta = c\left(\tan \dfrac{\theta}{2}\right)^{u/v}$. The result is $r\sin \theta = c\left(\tan \dfrac{\theta}{2}\right)^{u/v}$.

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