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Question
A train is moving on a circular track of 1500 m radius at the rate of 66 km/hr. What angle will it turn in 20 seconds?
Solution
Radius of the circular track r = 1500 m.
Speed of the train = 66 km/hr
Let θ be the angle made by the path of train at the centre in 20 seconds.
In 1 hr distance moved by train along the circular path = 66 km
In 60 × 60 seconds distance moved = 66 km
∴ In 20 seconds distance moved s = `66/(60 xx 60) xx 20`
s = `11/30` km
s = `11/30 xx 1000` meter
s = r θ
θ = `"s"/"r"`
θ = `(11/30 xx 1000)/1500` radians
= `(11 xx 1000)/(30 xx 1500)` radians
= `11/45` radians
= `(11/45 xx 180/pi)^circ`
= `11/5 xx 180/22 xx 7`
θ = 14°
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