Question

A boy takes 60 min to swim across a river. If his goal is to minimize to zero the distance that he is carried down stream. In both these attempts, the boy swims with the same speed relative to the river current. Which of the following statements can be true A) He can swim relative to water faster than the river current B) He can’t swim relative to water faster than the river current. C) If the width of the river is $3\sqrt{2}$ km , speed of river current is 4km/ h . D) If he crosses a $3\sqrt{2}$ km wide river in$60\sqrt{2}$ min he will be carried $\sqrt{2}$ km down stream

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11th

Physics

Motion in a Plane

Relative Motion in 2 Dimension

A boy swims in a straight l...

PHYSICS

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Asked on December 20, 2019 by

Sanchit Devgharkar

A boy swims in a straight line to reach the other side of a river. His velocity is 5 ms

−1

and the angle of swim with shore is 30

∘

. Flow of river opposes his movement at 2 ms

−1

. If width of river is 200 m, where does he reach the other bank roughly?

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VIDEO EXPLANATION

ANSWER

Velocity of river

v

r

=−2

i

^

Velocity of swimmer w.r.t river is

v

s

=5cos30

i

^

+5sin30

j

^

=4.33

i

^

+2.5

i

^

Using

v

R

=

v

s

+

v

r

, we get

v

R

=2.33

i

^

+2.5

j

^

Time taken by the swimmer=

ycomponentofvelocity

Distancealongy−axis

=

2.5

200

=80s

Distance moved along x-axis,

O

′

F=x component of relative velocity × time.

=2.33×80=186.4m

186m upstream

solution.

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