Question

A railway train is travelling on a circular curve of 1500 metres radius at the rate of 66 km/hr. Through what angle has it turned in 10 seconds?

Answer 1

Time = 10 seconds
Speed = $66\mathrm{km}/\mathrm{h}=\frac{66\times 1000}{3600}\mathrm{m}/\mathrm{s}$

$$\begin{gathered} \mathrm{We}\mathrm{know}: \\ \mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}} \\ \Rightarrow \frac{66\times 1000}{3600}=\frac{\mathrm{Distance}}{\mathrm{Time}} \\ \Rightarrow \mathrm{Distance}=\frac{66\times 1000}{3600}\times 10=\frac{1100}{6}\mathrm{m} \end{gathered}$$

Now,
Radius of the curve = 1500 m
$$\begin{gathered} \therefore \mathrm{\theta }=\frac{\mathrm{Arc}}{\mathrm{Radius}} \\ =\frac{{\displaystyle \frac{1100}{6}}}{1500} \\ =\frac{1100}{1500\times 6}=\frac{11}{90}\mathrm{radian} \end{gathered}$$
So, the train will turn $\frac{11}{90}$ radian in 10 seconds.