Not right on time

In an imaginary atmosphere, the air exerts a small force F F on any particle in the direction of the particle's motion. A particle of mass m m projected upward takes time t t in reaching the maximum height and time T T in the return journey to the original point.

Which of the following must be true?

t < T t < T t = T t = T t > T t > T t t and T T depend on the mass of the particle

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1 solution

Seth Christman
Dec 13, 2016

Since the air is exerting a force upwards during its trip to the maximum height, and gravity is still exerting a force downwards, the net force in the downward direction is less than the gravitational force (we assume a net force downwards otherwise there would be no maximum height).

On the particle's decent, it has both gravity and the air force both exerting in the downwards direction, meaning there is a net force greater than the gravitational force.

Since there is less net force during the ascent, it takes longer to reach the peak, meaning t > T t>T

What about the initial velocity?

Shaun Leong - 4 years, 6 months ago

Initial velocity shouldn't have any affect on the outcome, it would just increase both times by a similar amount

Seth Christman - 4 years, 6 months ago

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