Question

A helicopter takes off along the vertical with an acceleration a = 3 m/s² and Zero initial velocity. In a certain time t₁, the pilot switches off the engine. At the point of take-off, the sound dies away in a time t₂ =30 s.

Determine the velocity v of the helicopter at the moment when its engine is switched off, assuming that the velocity c of sound is 320 m/s.

Answer 1

At the moment the pilot switches off the engine, the helicopter is at an altitude h = at₁²/2. Since the sound can no longer be heard on the ground after a time t₂, we obtain the equation

where on the right-hand side we have the time of ascent of the helicopter to the altitude h and the time taken for the sound to reach the ground from the altitude h. Solving the obtained quadratic equation, we find that

We discard the second root of the equation since it has no physical meaning.

The velocity v of the helicopter at the instant when the engine is switched off can be found from the relation