A river is \(500m\) wide flows at a rate of \(4kmh^{-1}\). A swimmer who can swim at \(8kmh^{-1}\) in still water, wishes to cross the river straight then; (a) Along what direction must he strike? (b) What should be his resultant velocity? (c) What is the time of crossing the river?
Ans:(a) \(\theta=30^{o}\) (b) \(V_{Res}=4\sqrt{3}\frac{m}{s}\) and (c) \(t=260.4Sec\).
A person swims across the river which is flows with a velocity of \(3kmh^{-1}\) due east. If, the velocity of the person relative to water is \(4kmh^{-1}\) due north. Then; (i) What is his velocity relative to the shore of the river? (ii) How long does the person takes to cross the river if width of river is 1km? (iii) How far from his starting point will he reach the opposite bank?
Ans:(i) \(V_{pg}=5\frac{km}{h}\) & \(\theta=tan^{-1}\left(0.75\right)=36^{o}\) (ii) \(t=15min.\) and (iii) \(750m\).
A person rows a boat in a water with a speed of \(4 ms^{-1}\). Water in the river is flowing with a speed of \(2 ms^{-1}\). If, the person rows the boat perpendicular to the direction of flow. Find, resultant velocity of the boat and time taken by the boat to cross the river of the width of river is \(400m\).
Ans: \(V_{Res}=4.472\frac{m}{s}\)
Rain is falling vertically with a speed of \(35 ms^{-1}\). A women rides a bicycle with a speed of \(12 ms^{-1}\) from east to west direction. What is the direction in which she should hold the umbrella?
Ans: \(18^{o}\) with the vertical.
A person standing on a road has to hold his umbrella at \(60^{0}\) with the vertical to keep the rain away. Suddenly, he throughs his umbrella and starts running at \(20 ms^{-1}\), he finds that the rain drops are hitting his head vertically. Find, the speed of the rain drops with respect to (a) The road. (b) The moving man.
Ans: \(V_{rg}=23.1\frac {km}{h}\) and \(V_{rp}=11.55\frac {km}{h}\).
Wind is blowing at a speed of \(70 kmh^{-1}\) and the flag hoisted on a ship in a harbor flutters along north-east direction. If, the ship starts moving at a speed of \(50 kmh^{-1}\)towards north then what will be direction of fluttering of flag hoisted on ship?
Ans: \(\alpha=45.5^{o}\).
A bus is moving due east and a car is moving due north with the same speed of \(5 kmh^{-1}\) . what is the observed speed and direction of motion of car to the passengers in the bus?
Ans: \(V_{cb}=50\sqrt{2}\frac{km}{h}\) and \(\beta=45^{o}\).
A ship is streaming due west at \(10 ms^{-1}\). A boy runs across the deck at \(5 ms^{-1}\) in direction perpendicular to the direction of motion of the ship, which is towards north. What will be velocity of boy relative to sea?
Ans: \(V_{bs}=5\sqrt{5}\frac{m}{s}\) and \(\beta=tan^{-1}\left(0.5\right)=26^{o}\).
A river is flowing steadily with a speed of \(5 kmh^{-1}\). A boat mam can row with a speed of \(10 kmh^{-1}\) in still water. He rows the boat in river at right angle to the bank of the river. If, the width of the river is \(800 m\), then (i) How much time the boatman will take to cross the river? (ii) How far away from a point just opposite to the bank of the river he will be reaching there? (iii) What will be his effective speed?
Ans:(i) \(t=4.8min.\) (ii) \(400m\) and (iii) \(V_{Res}=5\sqrt{5}\frac{km}{h}\).
A swimmer crosses a flowing river of width \(d\) to and from in time \(t_{1}\). The time taken to cover the same distance up and down the stream is \(t_{2}\). If, \(t_{3}\) be the time that the swimmer would take to swim a distance of \(2d\) in still water then, Prove that; \(t_{1}^{2}=t_{2}.t_{3}\).
