A man directly crosses a river in time `t_1` and swims down the current a distance equal to the width of the river I time `t_2`. If `u and v` be the speed of the current and the man respectively, show that : `t_1 :t_2 = sqrt(v + u) : sqrt(v - u))`.

A man directly crosses a river in time `t_1` and swims down the curren

1.	A man directly crosses a river in time `t_1` and swims down the current a distance equal to the width of the river I time `t_2`. If `u and v` be the speed of the current and the man respectively, show that : `t_1 :t_2 = sqrt(v + u) : sqrt(v - u))`.
Answer» We know that the time taken foa a man to cross the river directly is given by `t_1 = (d)/(sqrt(v^2 - u^2))`, where `d` is the width of the river. Now, if the man swims downstream then the resultant velocity is `v + u`. The corresponding time, `t_2 = (d)/(u + v)`. Now, `(t_1)/(t_2) = (v+u)/(sqrt(v^2 - u^2))= (sqrt(v + u) sqrt(v + u))/(sqrt(v + u)sqrt(v - u)) rArr (t_1)/(t_2) = (sqrt(v + u))/(sqrt(v - u))`.

Discussion

No Comment Found

Related InterviewSolutions

From the top of at all building (height27.3m), a boy throws an apple upward, which strikes ground after 16 s. Take `g = 9.8 m//s^(2)`, find the speed of apple with which it was thrown and the maxium height reached by it.
A car travels along a straight line for first half time with speed `40 km//h` and the second half time with speed `60 km//h`. Find the average speed of the car.
A vechicle travels along a straight path between two places `alpha and beta`. It travels first half of the distance with a velocity of 72 km `h^(-1)` and the remaining distance with a velocity of 36 km `h^(-1)` then the average velocity of the vehicle is ______ m`s^(-1)` A. 11.3B. 13.3C. 15D. 14
In the case of a simple pendulum, a graph is drawn between the displacement and time taken for its oscillations as shown in the figure . Then From the given figure, the number of oscillation performed by the bob at the end of 21 s is ________ A. 3B. 4C. 2D. `3^(1//2)`
`{:("ColumnA","ColumnB"),(A. "Periodic motion",a."maximum displacement of vibrating particle from its mean position"),(B."Vibrtory motion" ,b."The pistion of a motor car engine at uniform car engine at uniform speed"),(C."Body at rest" ,c."Non- uniform motion"),(D."Amplitude",d.18//5 kmh^(-1)),(E."Variable speed" ,e."OScillating objects undergo change in shape of size"),(F. 1ms^(-1) , f. ("Total displacement")/("Total time")),(G."Average velocity" ,g. "Zero velocity"):}`
`{:( "Column A"," ColumnB"),(A. "Non- uniform motion","a. To measure speed of the vehicle"),(B."Oscillatory motion","b. Uniform motion"),(C."Mean position" , "c. A criket ball that rolls over ground"),(D."Speedometer","d.The needle of sewing machine that moves up and down"),(E."Constant speed","e. Freely suspended pendulum at rest"),(F. "Acceleration","f".("Total change in velocity")/("Total time taken for change")):}`
`{:( "Column A"," ColumnB"),(A."Speed",a."Uniform motion"),(B."Time",b."Non-uniform motion"),(C."Average speed",c."km h"^(-1)),(D."Uniform speed in a straight line",d."second"),("E. Freely falling body","e. Change in time period"),("F. Change in length of a pendulum","f".("Total distance")/("Total time")):}`
`{:("Column A" ,"ColumnB"),((A)"A body covers 5 m in every subsequent second",(a)"Lunar month"),((B)"Equal distances in unequal intervals of time",(b)"Non-uniform speed"),((C) "Periodic motion of the moon around the earth",(c)"Years"),((D)"Approprite unit to express the age of a person",(d) "Constant speed"):}`A. `A to b, B to c, C to d,D to a `B. `A to d, B to b, C to a, D to c`C. `A to d, B to a, C to b, D to c`D. ` A to a, B to b, C to c, D to d`
A ball thrown by one player reaches the other in `2 s`. The maximum height attained by the ball above the point of projection will be about.A. 2.5 mB. 5 mC. 7.5 mD. 10 m
A thief in a stolen car passes through a police check post at his top speed of `90 kmh^-1.` A motorcycle cop, reacting after 2 s, accelerates from rest at `5 ms^-2.` His top speed being `108 kmh^-1.` Find the maximum separation between policemen and thief.A. `112.5 m`B. `115 m` (c) 116.5 m (1) None of theseC. `116.5 m`D. None of these

A man directly crosses a river in time `t_1` and swims down the current a distance equal to the width of the river I time `t_2`. If `u and v` be the speed of the current and the man respectively, show that : `t_1 :t_2 = sqrt(v + u) : sqrt(v - u))`.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment