A man can swim at the rate of 10 km/hr in still water. A 2 km wide river
flows at the rate of 6 km/hr. The man wishes to swim across the river
directly opposite to the starting point. Then what will be his resultant
velocity and time taken to cross the river?
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2
Answer:
Answer
a. Velocity of man with respect to river water, v=5kmh
−1
. This is greater than the river flow velocity. Therefore, he can cross the river directly (along the shortest path or no drift condition from flow velocity). The angle of swim,
θ=
2
π
+sin
−1
(
v
u
)
=90
o
+sin
−1
(
v
u
)
=90
o
+sin
−1
(
5
3
)=90
o
+37
o
=127
o
w.r.t. the river flow or 37
o
w.r.t. the perpendicular in upstream direction
b. Resultant velocity or velocity of mass will be
v
m
=
v
2
−u
2
=
5
2
−3
2
=4kmh
−1
In the direction perpendicular to the river flow.
c. time taken to cross the river
t=
v
2
−u
2
d
=
4kmh
−1
1km
=
4
1
h=15min
piyushsheron:
thankyou
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