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JEE Main 2020 (4 Sep, Shift 2) · Inertia, First & Second Laws

Inertia, First & Second Laws question from JEE Main 2020 (4 Sep, Shift 2)

Q28JEE Main 2020 · 4 SEP · SHIFT 2Difficult

Inertia, First & Second Laws

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force mkv2 where v is its speed. The maximum height attained by the ball is:

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Answer: (c)

Going up, gravity and drag both act downward: $v\frac{dv}{dy} = -(g + kv^2)$ .
$H = \int_0^{u} \frac{v\,dv}{g + kv^2} = \frac{1}{2k}\ln(g + kv^2)\Big|_0^{u}$
$H = \frac{1}{2k}\ln\left(1 + \frac{ku^2}{g}\right)$
So the answer is (c).

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