  We consider a particle which moves on the x axis and is subject to a constant
force, such as gravity, plus a random force in the form of Gaussian white
noise. We analyze the statistics of first arrival at point $x_1$ of a particle
which starts at $x_0$ with velocity $v_0$. The probability that the particle
has not yet arrived at $x_1$ after a time $t$, the mean time of first arrival,
and the velocity distribution at first arrival are all considered. We also
study the statistics of the first return of the particle to its starting point.
Finally, we point out that the extreme-value statistics of the particle and the
first-passage statistics are closely related, and we derive the distribution of
the maximum displacement $m={\rm max}_t[x(t)]$.
