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?

Answer 1

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°