A train travels due south at $30 \mathrm{m} {\mathrm{s}}^{-1}$ ($1$ relative to the ground) in a rain that is blown towards the south by the wind. The path of each raindrop makes an angle of $70°$ with the vertical, as measured by an observer stationary on the ground on the ground. As an observer on the train, however, sees the drops fall perfectly vertically. Determine the speed of the raindrops relative to the ground.

In the overhead view of the figure, Jeeps $P$ and $B$ race along straight lines, across flat terrain, and past stationary border guard $A$. Relative to the guard. $B$ travels at a constant speed of $25.0 \mathrm{m} {\mathrm{s}}^{-1}$, at the angle ${\mathrm{\theta }}_2=30.0°$. Relative to the guard $P$ has accelerated from rest at a constant rate of $0.400 \mathrm{m} {\mathrm{s}}^{-2}$ at the angle ${\mathrm{\theta }}_1=60.0°$. At a certain time during the acceleration, $P$ has a speed of $40.0 \mathrm{m} {\mathrm{s}}^{-1}$. At that time, what are the $\left(a\right)$ magnitude and $\left(b\right)$ direction of the velocity of $P$ relative to $B$ and the $\left(c\right)$ magnitude and $\left(d\right)$ direction of the acceleration of $P$ relative to $B$?

Two ships, $A$ and $B$ leave to the port at the same time. The ship $A$ travels northwest at $24 \mathrm{knots}$ and $B$ travels at $28 \mathrm{knots}$ in a direction $40°$ west of the south $\left(1 \mathrm{knot}=1 \mathrm{nautical} \mathrm{mile} \mathrm{per} \mathrm{hour}\right)$. What are the $\left(a\right)$ magnitude and $\left(b\right)$ direction of the velocity of the ship $A$ relative to $B$? $\left(c\right)$ After what time will the ship be $160 \mathrm{nautical} \mathrm{miles}$ apart? $\left(d\right)$ What will be the bearing of $B$ (the direction of $B$'s position) relative to $A$ at that time?