Source: High School Physics Olympiad
Problem Sets:
Problem
Rain falls so that each raindrop moves uniformly in a straight line relative to the ground, falling vertically with speed $v$. A person rides in a car that moves in the $x$ direction with constant acceleration $a$. Observation starts at $t = 0$, when the car has speed $u_0$ and a raindrop is at height $y_0$ on the $y$-axis (directly above the car's position).
In the ground frame, the raindrop stays at $x = 0$ and falls as $y = y_0 - vt$. The car's position is $x_c = u_0 t + \frac{1}{2}at^2$.
The raindrop's coordinates relative to the car:
$$x' = 0 - x_c = -u_0 t - \frac{1}{2}at^2, \qquad y' = y_0 - vt$$From the second equation $t = \dfrac{y_0 - y'}{v}$. Substituting:
$$x' = -\frac{u_0}{v}(y_0 - y') - \frac{a}{2v^2}(y_0 - y')^2$$The trajectory relative to the car is a parabola (it would be a straight line only if $a = 0$).