A man can swim at a rate of $5 \mathrm{km} {\mathrm{h}}^{-1}$ in still water. A  $1 \mathrm{km}$ wide river flows at the rate of $3 \mathrm{km} {\mathrm{h}}^{-1}$. The man wishes to swim across the river directly opposite to the starting point.
(a) Along which direction must the man swim?
(b) What should be his resultant velocity?
(c) How much time will he take to cross the river?

A river is flowing with a speed of $1 \mathrm{km} {\mathrm{h}}^{-1}$. A swimmer wants to go to point $C$ starting from $A$. He swims with a speed of $5 \mathrm{km} {\mathrm{h}}^{-1}$ at an angle $\theta$ w.r.t. the river flow. If $AB=BC=400 \mathrm{m}$, at what angle with the river bank should the swimmer swim?

A man wants to swim in a river from $A$ to $B$ and back from $B$ to $A$ always following line $AB$. The distance between points $A$ and $B$ is $S$. The velocity of the river current $v$ is constant over the entire width of the river. The line $AB$ makes an angle $\alpha$ with the direction of current. The man moves with velocity $u$ at angle $\beta$ to the line $AB$. The man swim to cover distance $AB$ and back, find the time taken to complete the journey.

A man walking due east with $3 \mathrm{km}/\mathrm{hr}$ observes rain falling vertically at the rate of $3 \mathrm{km}/\mathrm{hr}$. Find the actual speed and direction of the rain with respect to ground.

A person standing on a road has to hold his umbrella at $60°$ with the vertical to keep the rain away. He throws the umbrella and starts running at $20{ \mathrm{m} \mathrm{s}}^{-1}$. He find that rain drops are hitting his head vertically. Find the speed of the rain drops with respect to

(a) the road and

(b) the moving person.