Past exam of the physics 1 paper of the University of Oxford / 2017 resit / 7

Choose upward velocity positive during ascent. Gravity and linear drag both point downward, giving the linear differential equationAt the highest point $v=0$, soThe vertical ascent under linear drag time is smaller than $v_0/g$ for $\alpha >0$, because $\log (1+x)<x$. Its zero-drag limit is $v_0/g$, as required by constant-gravity projectile motion.