JEE Physics/ Lakshmikanta Satapathy/ Kinematics of Particles QA part 7/ JEE Question on Man crossing a flowing river in shortest distance and in shortest time solved with the related concepts

1. Physics Helpline
L K Satapathy
Kinematics QA 7
Man crossing River Problem

v
v/2vcos

2. Physics Helpline
L K Satapathy
Kinematics QA 7
Answer :
Question : A man can swim in still water with speed v and the river water
is flowing with speed v/2 . The times taken by him to cross the river in the
shortest distance and the shortest time respectively are t1 and t2 . Then the
ratio t2 / t1 is

v
O v/2
A P
vcos
vsin
X X
Speed of the man in still water = v
Speed of the river water towards right = v/2
Let the man strike along OA to cross the river
Let  AOX = 
Velocity components (i) v sin along OP
31 1 1( ) ( ) ( ) ( )
4 2 22
a b c d
(ii) v cos along OX
Let the width of the river OP = S

3. Physics Helpline
L K Satapathy
Kinematics QA 7
v
O v/2
P Q
X
Crossing in shortest distance  no motion along the river
(t) is minimum when sin is maximum (=1)
 Time to cross the river in shortest time
Correct option = (d)
1
2 . . . (1)
sin 3
S St
v v
  
2 . . . (2)St
v

2
1
3 3(1)& [
2
](2)
2
t vS
t v
A
S
ns   
sin
St
v 
 Time taken to cross the river
1cos cos 60
2 2
ovv        

4. Physics Helpline
L K Satapathy
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