Question

Phelps crosses Hudson river along a line making an angle 45°
with the direction of flow. Velocity of flowing water is 5 m/s. If he
takes 12 seconds to cross the river. Then velocity of Phelps with
respect to water will be: [width of river = 60 m]
5 ms
5 m/s
5,5 m/s
10 m/s​

Answer 1

Given : Phelps crosses Hudson river along a line making an angle 45°

with the direction of flow. Velocity of flowing water is 5 m/s.

takes 12 seconds to cross the river.

To Find : velocity of Phelps with  respect to water will be

Solution:

Velocity  of Swimmer = V

angle of 45° with flow    

Velocity component in direction of  crossing

V/√2

12 x  V/√2 = 60

=> V = 5√2

Velocity along flow  5 m/s

Velocity of flowing water is 5 m/s.

Hence Velocity of Swimmer  with   respect to water  along flow = 5 - 5 = 0

Velocity of Swimmer  with   respect to water  along crossing = 5 m/s

Velocity of Swimmer   with   respect to water = 5 m/s

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Answer 2

HELLO DEAR,

GIVEN:- Phelps crosses Hudsen river alongs a line making an angle of 45° with restect to flowing river in the direction of flow of river.

The time taken to cross the flowing river by Phelps = 12 second.

The widht of river = 60 meter.

To find the velocity of Phelps with respect to flowing water river.

ANSWER:-

Option (D) 10 m/s.

Let the velocity of swimmer in the river with an angle if 45° with flowing water = V

Taking the components of velocity of swimmer along the bank of river ,

We get Vsin45°

= V/√2

And width of river = 60m

Time taken by swimmer to cross the river = 12s.

Si, by using the relation

Speed = distance/time

V/√2 = 60/12

V/√2 = 5

V= 5√2.

And velocity of components of swimmer alongs of the horizontal river = V/√2

= 5√2/√2

= 5 m/s

Therefore,

Then velocity of Phelps with

respect to water will be:

(5+5)m/s = 10m/s.

Because they both are in opposite direction.

I HOPE IT'S HELP YOU DEAR,

THANKS.