A steam boat goes across a lake and
comes back (a) On a quite day when the
water is still and (b) On a rough day when
there is uniform air current so as to help
the journey onward and to impede the
journey back if the speed of the launch
on both days was same, in which case it
will complete the journey in lesser time
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Answer:
If the breadth o fthe lake is l and velocity of boat is v. Time in gpoing and coming back on a quite day
t
Q
=
ν
b
l
+
ν
b
l
=
ν
b
2l
....(i)
Now if ν i sthe velocity of air-current then time taken in going across the lake.
t
1
=
ν
b
+ν
a
1
[As current helps the motion]
and time taken in coming back t
2
=
ν
b
−ν
a
l
[As current helps the motion]
So t
R
=t
1
+t
2
=
ν
b
[1−(ν
a
/ν
b
)
2
]
2l
....(ii)
From equation (i) and (ii)
t
Q
t
R
=
[1−(ν
a
/ν
b
)
2
]
1
>1 [as 1−
ν
b
2
ν
a
2
<1] i.e. t
R
>t
Q
i.e time taken to complete the journey on quit day is lesser than that on rough day.
Explanation:
thanks please mark as brillent thanks
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