A high-speed train, weighing $P=150$ tons, travels at a maximum speed of $v=72 \frac{\mathrm{km}}{\text { hour }}$ on a horizontal track where $\rho=0,005$. At what speed can it travel on a track that has the same friction conditions but an elevation of $e=0,030$? [^0]


[^0]:    ${ }^{1}$ In this problem, $\rho$ is the coefficient of friction, and $e$ is the sine of the incline angle.
The works performed in equal times on two tracks are equal, so if $u$ represents the sought speed, then

$$
\rho \cdot u \cdot p+e \cdot u \cdot p=\rho \cdot p \cdot v
$$

from this

$$
u=\frac{\rho \cdot v}{\rho+e}
$$

whatever unit we substitute for $v$, we get $u$ in the same unit.

$$
u=2.587 \frac{\mathrm{m}}{\mathrm{sec}}=10.3 \frac{\mathrm{km}}{\text { hour }}
$$

The problem was solved by: Bánó L., Blum J., Csada I., Földes R., Fodor H., Gráf V., Ehrenstein P., Grünhut H., Haar A., Jánosy Gy., Merse P., Schwarz O., Székely J.