A man is crossing a river flowing with a velo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $v$ be the velocity of the man in still water and $u = 5 \ m/s$ be the velocity of the river flow.To reach a point directly across,the man mus

Vedclass · Accepted Answer

$13$

Vedclass · Answer

(B) Let $v$ be the velocity of the man in still water and $u = 5 \ m/s$ be the velocity of the river flow.To reach a point directly across,the man must swim at an angle such that his resultant velocity is perpendicular to the river flow.The effective velocity of the man across the river is $v_{eff} = \sqrt{v^2 - u^2}$.The time taken to cross the river is given by $t = \frac{d}{v_{eff}}$,where $d = 60 \ m$ is the width of the river.Substituting the given values: $5 = \frac{60}{\sqrt{v^2 - 5^2}}$.$\sqrt{v^2 - 25} = \frac{60}{5} = 12$.Squaring both sides: $v^2 - 25 = 144$.$v^2 = 144 + 25 = 169$.$v = \sqrt{169} = 13 \ m/s$.

$A$ man is crossing a river flowing with a velocity of $5 \ m/s$. He reaches a point directly across at a distance of $60 \ m$ in $5 \ s$. His velocity in still water should be: (in $m/s$)

Similar Questions

$A$ train of $150 \; m$ length is going towards the north direction at a speed of $10 \; m/s$. $A$ parrot flies at a speed of $5 \; m/s$ towards the south direction parallel to the railway track. The time taken by the parrot to cross the train is: (in $; s$)

$A$ boat is sent across a river with a velocity of $8 \, km/hr$. If the resultant velocity of the boat is $10 \, km/hr$,then the velocity of the river is ........ $km/hr$.

Two cars are moving in the same direction with the same speed $30 \, km/hr$. They are separated by a distance of $5 \, km$. The speed of a car moving in the opposite direction,if it meets these two cars at an interval of $4 \, minutes$,will be.......$km/hr$.

Rain is falling vertically with a speed of $35 \; m s^{-1}$. $A$ woman rides a bicycle with a speed of $12 \; m s^{-1}$ in the east to west direction. What is the direction in which she should hold her umbrella?

The stream of a river is flowing with a speed of $2\,km/h$. $A$ swimmer can swim at a speed of $4\,km/h$. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight (in $^\circ$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module