In an imaginary atmosphere, the air applies a small force F on a particle in the direction of its motion. A particle of mass m projected upward requires a time t₁ to reach its maximum height and a time t₂ for its return journey to the starting point. It follows that

Step-by-step solution

During the upward journey, the particle moves upward, so the force F acts upward. The gravitational force mg acts downward. The net downward acceleration during ascent is a₁ = g - F m . Let the maximum height reached be h . The time of ascent t₁ is given by the kinematic equation h = 1 2 a₁ t₁^2 , which gives t₁ = 2h a₁ . During the downward journey, the particle moves downward, so the force F acts downward. The gravitational force mg also acts downward. The net downward acceleration during descent is a₂ = g + F m