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JEE Main20204 Sep 2020Evening ShiftPhysicsMotion in One DimensionActual

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force m k v 2 where v is it speed. The maximum height attained by the ball is :

Options

  1. A1 2 k tan - 1 k u 2 g
  2. B1 k ln 1 + k u 2 2 g
  3. C1 k tan - 1 k u 2 2 g
  4. D1 2 k ln 1 + k u 2 g

Correct answer

D. 1 2 k ln 1 + k u 2 g

Step-by-step solution

F ne  = ma - mg - mkv 2 = mv dv ds v dv ds = - g - kv 2 - ∫ v 0 0 vdv g + kv 2 = ∫ 0 h ds = h max h max = 1 2 K in g + kv 0 2 g

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