Question

A train is travelling on a curve of $700$m radius at $14$km/hr. Through what angle will it turn in one minute.

Answer 1

Given: Radius ($r$) = $700$m, Speed of the train = $14$km/hr and Time taken ($t$) = $1$ min

Now, Distance covered by the train in $1$ min will be given by,

Distance = Speed $\times$ Time

$\therefore$ Distance covered = $700\times \frac{1}{60}\times 1000=\frac{14000}{60}$ m [$1$ min =$\frac{1}{60}$ seconds]

Now, Length of the arc covered = Distance covered by train in $1$ min

$\Rightarrow \frac{\theta }{{360}^{\circ }}\times 2\pi r=\frac{14000}{60}$ [where $\theta$ is the required angle]

$\Rightarrow \frac{\theta }{{360}^{\circ }}\times 2\times \frac{22}{7}\times 700=\frac{14000}{60}$

$\Rightarrow \theta =\frac{{210}^{\circ }}{11}$

Thus, the train will turn $\frac{{210}^{\circ }}{11}$ in $1$ min.