# A railway train is travelling on a circular curve of 1500 metres radius at the rate of 66 km/hr.

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?

Solution:

Time = 10 seconds

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

We know,

Speed $=\frac{\text { Distance }}{\text { Time }}$

$\Rightarrow \frac{66 \times 1000}{3600}=\frac{\text { Distance }}{\text { Time }}$

$\Rightarrow$ Distance $=\frac{66 \times 1000}{3600} \times 10=\frac{1100}{6} \mathrm{~m}$

Now,

Radius of the curve = 1500 m

$\therefore \theta=\frac{\text { Arc }}{\text { Radius }}$

$=\frac{\frac{1100}{6}}{1500}$

$=\frac{1100}{1500 \times 6}=\frac{11}{90}$ radian

So, the train will turn $\frac{11}{90}$ radian in 10 seconds.