Embibe Experts Solutions for Exercise 5: EXERCISE

A man desires to swim across the river in shortest time. The velocity of river water is $3 \mathrm{km}{ \mathrm{h}}^{-1}.$ He can swim in still water at $6 \mathrm{km}{ \mathrm{h}}^{-1}.$ At what angle with the velocity of flow of the river should he swim?

A man standing on a road has to hold his umbrella at $30°$ with the vertical to keep the rain away. He throws the umbrella and starts running at $5 \mathrm{km}/\mathrm{h}.$ Now he finds that raindrops are hitting his head vertically. Find the speed of the raindrops w.r.t.

(i) The road
(ii) The moving man.

Two ships are $10 \mathrm{km}$ apart on a line running south to north. The one farther north is steaming west at $40 \mathrm{km}/\mathrm{hr}.$ The other is steaming north at $40 \mathrm{km}/\mathrm{hr}.$ What is their distance of closest approach (in $\mathrm{km}$ ) and how long do they take to reach it?

A man can swim at $4 \mathrm{m} {\mathrm{s}}^{-1}$ in a still water swimming pool. He enters a $200 \mathrm{m}$ wide river at one bank and swims (w.r.t. water) at an angle of $60°$ to the river flow velocity. The river flow velocity is $5 \mathrm{m} {\mathrm{s}}^{-1}.$ In how much time does he cross the river? Calculate his drift.

A car drives due north at $50 \mathrm{km}/\mathrm{hr}.$ Wind blows due North-West at $50\sqrt{2} \mathrm{km}/\mathrm{hr}.$ In what direction, a flag hoisted on the roof of the car points?