9. Two boats A and B moved away from a buoy anchored
in the middle of a river. A moved along the river and B
at right angle to it. Having moved off equal distances
from the buoy, the boats returned. Find the ratio of the
times of motion of the boats, if the velocity of each
boat with respect to still water is times greater than
the velocity of water current.
n
Answers
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Explanation:
Let l be the distance covered by the boat A along the river as well as by the boat B across the river. Let v
0
be the stream velocity and v
′
the velocity of each boat with respect water. Therefore time taken by the boat A in its journey
t
A
=
v
′
+v
0
l
+
v
′
−v
0
l
and for the boat B t
B
=
v
′
2
−v
0
2
l
+
v
′
2
−v
0
2
l
=
v
′
2
−v
0
2
2l
Hence,
t
B
t
A
=
v
′
2
−v
0
2
v
′
=
η
2
−1
η
(whereη=
v
v
′
)
On substitution
t
B
t
A
=1.8
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