Problem 1.349

A rod moves along a ruler with a constant velocity. When the positions of both ends of the rod are marked simultaneously in the reference frame fixed to the ruler, the difference of readings on the ruler is equal to \(\Delta x_{1}=4.0 \mathrm{~m} .\) But when the positions of the rod's ends are marked simultaneously in the reference frame fixed to the rod, the difference of readings on the same ruler is equal to \(\Delta x_{2}\) \(=9.0 \mathrm{~m} .\) Find the proper length of the rod and its velocity relative to the ruler.