A rod flies with constant velocity past a mark which is stationary in the reference frame $K$. In the frame $K$ it takes $\Delta t=20ns$ for the rod to fly past the mark. In the reference frame fixed to the rod the mark moves past the rod for $\Delta t^{\prime }=25ns$. Find the proper length of the rod.

Q. A rod moves lengthwise with a constant velocity $v$ relative to the inertial reference frame $K$. At what value of $v$ will the length of the rod in this frame be $\eta =0.5\%$ less than its proper length?

Q. Two rods of the same proper length $l_0$ move toward each other parallel to a common horizontal axis. In the reference frame fixed to one of the rods the time interval between the moments, when the right and left ends of the rods coincide, is equal to $\Delta t$. What is the velocity of one rod relative to the other?

Q. Find the proper length of a rod if in the laboratory frame of reference its velocity is $v=\frac{c}{2}$, the length $l=1.00m$, and the angle between the rod and its direction of motion is $\theta ={45}^{\circ }$.

Q. Find what time interval should separate the markings of coordinates of the rod's ends in the frame $K$ for the difference of coordinates to become equal to the proper length of the rod.

Q. With what velocity (relative to the reference frame $K$) did the clock move, if during the time interval $t=5.0s$, measured by the clock of the frame $K$, it became slow by $\Delta t=0.10s$?