If a train moves on a railway track of radius 1.5 km at the rate of 66 km/hr. Find out the anglethrough which it will turn in 10 seconds.
Answers
We have, In circular track,
O
A
=
O
B
=
r
=
1500
m
∠
A
O
B
=
θ
= angle the train turns in 10 seconds
Speed of train
=
66
k
m
/
h
r
=
66
×
1000
60
×
60
m
/
s
e
c
[Since,
1
h
r
=
60
×
60
seconds]
=
110
6
m
/
s
e
c
Since,
speed
=
Distance
Time
So, distance travelled in
10
sec
=
Speed
×
Time
∴
Train will travel in 10 sec
=
110
6
×
10
=
1100
6
m
As train travelled in circular motion, so the distance becomes arc length of the circle.
∴
arc~A
=
1100
6
m
Thus,
θ
=
arc
radius
=
1100
6
×
1500
=
11
90
radian
∴
The train will turn by
(
11
90
)
radians angle in 10 sec.
MathematicsRD SharmaStandard XII
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