JEE Main · PhysicsHard

$A body of mass $m$ is projected vertically upwards with velocity $v_0$. If it experiences a resistive force proportional to its velocity, $F = -kv$, what is the maximum height reached by the body?$

Show correct answer & step-by-step solution

Correct answer: B — $\frac{mv_0}{k} - \frac{m^2g}{k^2} \ln(1 + \frac{kv_0}{mg})$

Solution

Set up the equation of motion

m \frac{d v}{d t} = - m g - k v

. Use the chain rule

\frac{d v}{d t} = v \frac{d v}{d y}

to integrate

\int_{v_{0}}^{0} \frac{m v d v}{- m g - k v} = \int_{0}^{H} d y

to find the maximum height

H