Question

The train has to negotiate the 400m by how much should the outer rail be raised with respect to the inner rail for the speed of 48km/hr?the distance between the rails is 1m.

Answer 1

$$\begin{gathered} \mathrm{Speed}: \\ \mathrm{v}=48\mathrm{km}/\mathrm{h} \\ =48\times \frac{5}{18}\mathrm{m}/\mathrm{s} \\ =13.3\mathrm{m}/\mathrm{s} \\ \mathrm{tan\theta }=\frac{{\mathrm{v}}^2}{\mathrm{rg}} \\ \mathrm{But},\mathrm{tan\theta }=\frac{\mathrm{h}}{\mathrm{L}} \\ \frac{\mathrm{h}}{\mathrm{L}}=\frac{{\mathrm{v}}^2}{\mathrm{rg}} \\ \mathrm{h}=\frac{{\mathrm{v}}^2\mathrm{L}}{\mathrm{rg}} \\ =\frac{13.3^2\times 1}{400\times 9.8} \\ =0.045\mathrm{m} \\ \mathbf{}\mathbf{}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{cm} \end{gathered}$$