A train is moving with a speed of 12 m s - 1 on rails which are 1 . 5 m apart. To negotiate a curve radius…

For the train, moving along the curved rails, it can be written, with reference to the figure below, that

$\tan \theta =\frac{v^2}{Rg} ...\left(1\right)$

Also, from the above figure, it follows that

$\tan \theta =\frac{h}{1.5} ...\left(2\right)$

Equations (1) and (2) imply that

$$\begin{gathered} \frac{h}{1.5}=\frac{v^2}{Rg} \\ \Rightarrow h=1.5\times \frac{{\displaystyle v^2}}{{\displaystyle Rg}} \\ =1.5\times \frac{{\displaystyle {\left(12 \mathrm{m} {\mathrm{s}}^{-1}\right)}^2}}{400 \mathrm{m}\times 10 \mathrm{m} {\mathrm{s}}^{-2}} \\ =0.054 \mathrm{m} \\ =5.4 \mathrm{cm} \end{gathered}$$