# The Imaginary Atmosphere!

**Classical Mechanics**Level 3

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 \(t_2\)?

**Assumptions**

- 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.