Past exam of the physics 1 paper of the University of Oxford / 2017 resit / 8 / c / Solution

Height decreases at rate $\dot{h}=-v$. Set $m=m_0-\alpha t$; an antiderivative needed for the rocket equation isConsequentlyDifferentiating this expression recovers $\dot{h}=-v$ and substituting $t=0$ gives $h(0)=h_0$, which check both the sign and the integration constant.