MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Apparent Depth

A swimmer cro...

Question

A swimmer crosses a flowing stream of width $^{'} ω^{'}$ to and fro in time $t_{1}$ . The time taken to cover the same distance up & down the stream is $t_{2}$ . if $t_{3}$ is the time swimmer would take to swim a distance $2 ω$ in still water, then:

A

t_{1}^{2} = t_{2} t_{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

t_{2}^{2} = t_{1} t_{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

t_{3}^{2} = t_{1} t_{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

t_{3} = t_{1} + t_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $t_{1}^{2} = t_{2} t_{3}$
Let 'u' be the velocity of swimmer in still water and 'v' be velocity of river.

in case 1
Since v and u are perpendicular to each other.
$t_{1} = 2 (\frac{w}{\sqrt{u^{2} - v^{2}}})$

In case 2nd
The swimmer goes upstream and downstream.
$t_{2} = \frac{w}{u + t} + \frac{w}{u - t} = \frac{2 u w}{u^{2} - v^{2}}$

In case 3rd
Still water
$t_{3} = \frac{2 w}{4}$
We see $t_{1}^{2} = t_{2} t_{3}$

Hence option (A) is correct

Suggest Corrections

thumbs-up

1

Similar questions

Q. A boat covers certain distance between two spots on a river taking

^{'} t_{1}^{'}

time, going down stream and

^{'} t_{2}^{'}

time going upstream, what time will be taken by the boat to cover the same distance in still water :-

Q. A swimmer can swim with a speed

v

If the swimmer crosses a swimming pool of width

^{'} d^{'}

A

to directly opposite point

B

on other side in time

t_{1}

as shown in figure and in a flowing river (river velocity

u

) of same width

^{'} d^{'}

A^{'}

to directly opposite point

B^{'}

on other bank in time

t_{2}

(\frac{t_{1}}{t_{2}})

is equal to: (Assume

v > u

)

Q. A swimmer can swim with a speed

v

in still water.

If the speed of the river flow is

u

and the time taken by swimmer to reach opposite point on other bank of the river is

T_{1}

and the time taken to travel an equal distance upstream (against the water current) in the river is

T_{2}

\frac{T_{2}}{T_{1}}

will have a value

Q. A swimmer can swim with a speed

v

If the swimmer crosses a swimming pool of width

^{'} d^{'}

A

to directly opposite point

B

on other side in time

t_{1}

as shown in figure and in a flowing river (river velocity

u

) of same width

^{'} d^{'}

A^{'}

to directly opposite point

B^{'}

on other bank in time

t_{2}

(\frac{t_{1}}{t_{2}})

is equal to: (Assume

v > u

)

Q. In a G.P. of real numbers, it is given that

T_{1} + T_{2} + T_{3} + T_{4} = 30

T_{1}^{2} + T_{2}^{2} + T_{3}^{2} + T_{4}^{2} = 340

. Determine the G.P.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Apparent Depth

PHYSICS

Watch in App

explore_more_icon

Explore more

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon