a man can swim at the rate of 10km/hr in still water . a 800m wide river flows at a rate of 6km/hr. the man wishes to swim across the river along the shortest path .time taken by men to cross the river is
a) 15min
b) 3min
c) 2min
d) 6min
Answers
Answer:
a
Explanation:
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
ANSWER
Let the angle between the swimmer and the perpendicular to the flow of river is θ with the perpendicular to the flow of river and time to cross the river is t
(i)
The direction is given as,
sinθ=
10
5
θ=30
∘
(ii)
The resultant velocity is given as,
V=V
sg
cos30
∘
=10cos30
∘
=8.66km/h
(iii)
Displacement in vertical direction is given as,
(V
sg
cosθ)t=800×10
−3
(10cos30
∘
)t=800×10
−3
t=0.092s
t=5.5min
Explanation:
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