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A railway train is travelling on a curve of 750m radius at 30km/hr through to what angle it turns in 10 second.

Answer
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Hint:
First of all we’ll use the distance formula which is Distance formula =Speed×Time, to get the distance travelled by train in 10 seconds. And then by using formula arc length formula; θ=arc lengthradius=lr, we’ll get the required answer. In the above mentioned formula l represents arc length, r represents the radius of the circle and θ represents the angle in radians made by the arc at the centre of the circle.

Complete step by step solution:
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Given: Radius of the curve =750 m.
Speed at the railway train in travelling =30km/hr
=30×10003600m/s=30×518m/s=15018m/s
Distance travelled by the train in 10 second;
=Distance=Speed×Time
=Distance=Speed×TimeDistance=15018×10mDistance=2503m
Now, using Arc length formula; θ=arc lengthradius
θ=2503750radianθ=2503×1750radianθ=19radian

The train will make an angle of 19radian.

Note:
This is a classic problem connecting our real life to mathematics. In higher studies, the same question can be asked with a slight change. They’ll give a certain condition and say the train is running on the path which follows this condition. We have to find the path of the train. This kind of problem can be solved by locus concept.