A particle is projected vertically upward in a medium with quadratic air resistance and later returns to the same level. Which statements are correct?
Select all that apply

Question

A particle is projected vertically upward in a medium with quadratic air resistance and later returns to the same level. Which statements are correct?

G1 Physics · Accepted Answer

For quadratic drag: ascent time = (V/g)tan⁻¹(u/V), while descent time = (V/g)sinh⁻¹(u/V). For positive u/V, sinh⁻¹z > tan⁻¹z, so descent time>ascent time. The impact speed is u/√[1+(u/V)²] < u. The upward drag increases the effective downward acceleration, so the maximum height is less than the vacuum value u²/(2g). Because drag always opposes motion, the upward and downward equations are different; the motion is not symmetric. Hence A, B and C are correct.