A man ina boat rowing away from light house 200m high takes 2 minutda to change the angle of elevation of the top of the lighthouse from 60degree to 45degree find the speed of the boat 10 th class
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Answer:
Correct option is B)
Height of light-house = 100 m
Time taken to change the angle of elevation from 60
∘
and 45
∘
= 2 minutes
Let the distance from the light house be d
a
, d
b
when the angle of elevation be 60
∘
and 45
∘
respectively
Thus, tanθ =
distancefromlighthouse
height
Thus, tan60=
d
a
100
⇒d
a
=
3
100
and, tan45=
d
b
100
⇒d
b
=100
∴ Distance travelled =100−
3
100
=42.2 m
Speed=
2×60
42.2
s
m
{∵Speed=
time
distance
}
To change
s
m
to
hr
km
we need to multiply by
5
18
∴Speed=(
2×60
42.2
×
5
18
)
hr
km
Hence the Speed=1.269
hr
km
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