A boat moves relative to water with a velocity $v$ which is $n$ times less than the river flow velocity $u$. At what angle to the stream direction must the boat move to minimise drifting?

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.

A man is coming down an incline of angle $30°$. When he walks with speed $2\sqrt{3} \mathrm{m}{ \mathrm{s}}^{-1}$, he has to keep his umbrella vertical to protect himself from rain. The actual speed of rain is $5{ \mathrm{m} \mathrm{s}}^{-1}$. At what angle with vertical should he keep his umbrella when he is at rest so that he does not get drenched?