Question

A train is running on a circular track of radius 1 km at the rate of 36 km per hour. Find the angle, to the nearest minute, through which it will turn in 30 seconds.

Answer 1

Radius of circular track$=r=1km$

Circumference$=2\pi r=2\pi km$

Speed of train$=36$ km\hr

Distance moved by train in 30 seconds $=36\times \frac{30}{3600}$

$=\frac{3}{10}$ km

For $2\pi$ km, train turns $2{\pi }^c$

$\therefore$ For $\frac{3}{10}$ km, train turns ${\frac{3}{10}}^c={\frac{54}{\pi }}^{\circ }$

1 minute of arc$={\frac{1}{60}}^{\circ }$

Angle turned by train $=\left(\frac{54\times 60}{\pi }\right)$ minutes of arc.

$\simeq 1031$ minutes