IIT JEE , AIEEE Forum - Physics , Mechanics

rshm15varma

A boat has speed 5km/hr in still water.river width=1 km.boat travels along the shortest possible path in 15 min.The velocity of river?

ans) Distance covered in 15 minutes=1.25km

drift by boat=sqr root of (1.25²-1²)=0.75 km

therefore,steering angle: sin theta=3/5

drift=x=time*(velocity along drift directn i.e. x-axis)

.75=15/60*(v_r-v_brsintheta)

putting the values we get

v_r=velocity of river=6km/hr

but anser is 3km/hr.

helpppppppppp

namangu

since the shortest distance will be perp. to river and is thus 1 km ,rivers width

so speed of boat in dir. of motion = 1/15 km/min=4km/h

since the absolute velocity of river is 5 km/h

4*4+x*x=5*5
x=3km/h

so speed of boat per. to motion will be 3 km/h and wll be equal to velocty of river

namangu

yur assum. tat the dis. covere is 1.25 is not correct as you have not considered river
flow

rate me plzzzz

rshm15varma

hellooooooooooo,that's not y assummption,that is by calculation:

distance covered in 15 minutes by boat=(15/60*5)=1.25km

help ppll

catch_arnnie

why are r making you the problem so complicated by takin' drift & all that???

just be simple in your approach

solution::

let the angle of boat with the width of the river be theta

so, velocity of boat along the width of the river is 5cos theta

5 cos theta = distance/time
5cos theta = 1/(1/4)
=> cos theta = 4/5

=> sin theta = 3/5

for shortest path, the drift has to be zero.

so, velocity of boat against the river = velocity of river(v)
5 sin theta = v

=> river water velocity = 3 kmph

shanks

This is the case of no drifting.

By the problem:-

5sinx*1/4=1
sinx=4/5
cosx=3/5

the speed of river is 5cosx=3Km/h. (as their is no drifting).
Here x is the angle between the velocity of the boat and the velocity of river.

Rate me ifyou find the answer satisfactory.

shobna

hi, u r wrong at d point where u find d distance covered.
d component of vel of boat along vertical y axis will help d boat to move d shortest dist.

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