The Imaginary Atmosphere!

Classical Mechanics Level 2

In an imaginary atmosphere, the air exerts a small force \(F\) on any particle in the direction of the particle's motion. A particle of mass \(m\) is projected vertically upwards take time \(t_1\) in reaching the maximum height and time \(t_2\) in returning to the original point.

Which of the following relations hold concerning \(t_1\), and \(t_2\)?


  • Assume the forces are such that the particle returns to Earth.
  • The drag force is an increasing function of \(v\) and always opposes the motion of the particle.

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