The Imaginary Atmosphere!
In an imaginary atmosphere, the air exerts a small force on any particle in the direction of the particle's motion. A particle of mass is projected vertically upwards take time in reaching the maximum height and time in returning to the original point.
Which of the following relations hold concerning , and ?
Assumptions
- Assume the forces are such that the particle returns to Earth.
- The drag force is an increasing function of and always opposes the motion of the particle.
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1 solution
While the object moves upwards, it would be helped by the imaginary force, but opposed by gravity. But, when it comes down, It is helped by the imaginary force, which is applied in the direction of motion, and also by gravity. Due to these two forces its velocity increases and its downward time, t2 becomes less than its upward time i.e. t1.