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KVPY2017MathematicsHyperbola

The sound of a cannon firing is heard one second later at a position B than at position A . If the speed of sound is uniform, then

Options

  1. AThe positions A and B are foci of a hyperbola, with cannon's position on one branch of the hyperbola
  2. Bthe position A and B are foci of an ellipse with cannon's position on the ellipse
  3. COne of the positions A, B is focus of a parabola with cannon's position on the parabola
  4. DIt is not possible to describe the positions of A, B and the cannon with the given information

Correct answer

A. The positions A and B are foci of a hyperbola, with cannon's position on one branch of the hyperbola

Step-by-step solution

PB - PA = Vt + v - vt PB - PA = V (const) locus of P is Hyperbola A & B are foci of Hyperbola

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