# The Imaginary Atmosphere!

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.
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