Math Help - Non-dimensional differential equation

1. Non-dimensional differential equation

Consider non-dimensional equation for the height at the highest point is given by
$$h(\mu)= \frac{1}{\mu}- \frac{1}{\mu^2} \log_e(1+\mu)$$
$0<\mu\ll 1.$
Determine to $O(\mu)$, the (non-dimensional) time for the body to travel from the highest point to the ground, and determine an estimate for the (non-dimensional) speed of the body when it returns to the ground, again to $O(\mu)$.