Question

In an imaginary atmosphere, the air exerts a small force F on any particle in the direction of the particle's motion.

Answer 1

In this imaginary atmosphere force due to air is in the motion of the body so it will support the motion.

When a particle moves upwards the force of air supports it in upward direction but gravitational pull oppose its motion and act downwards. Now when the particle moves downwards force of air as well as gravitational pull supports it so the time taken by the particle in this case will be less (as both the forces supporting particle to move downwards, its velocity increases) than the time taken by the particle to move upwards. So,

 t1>t2