Principle of Mathematical Induction

Principle of Mathematical Induction

Question

A railway train is travelling on a circular track of 1500 m radius at the speed of 66 km/h. Through what angle (in degrees) does it turn in 10 seconds ?

Answer

Radius of the circular track, r = 1500 m
Distance travelled in 1h or 60 space cross times space 60 space sec space equals space 66 space km space or space 66000 space straight m
Distance travelled by train in 1 sec = fraction numerator 66000 over denominator 60 cross times 60 end fraction straight m space equals space 55 over 3 straight m
Length of arc = Distance travelled by the train in 10 seconds = space space 55 over 3 space cross times space 10 space straight m space equals space 550 over 3 straight m
Using l over r space equals space theta comma we get space space straight theta space equals space open parentheses 550 over 3 cross times space 1 over 1500 close parentheses to the power of straight c space equals space open parentheses 11 over 90 close parentheses to the power of straight c space equals space open parentheses 11 over 90 cross times space 180 over straight pi close parentheses to the power of ring operator space equals space open parentheses 11 over 90 cross times 180 space cross times 7 over 22 close parentheses to the power of ring operator space equals space 7 degree

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