$1.1.8.$ The conveyor belt has speed $w$. Above the belt moves a machine, throwing $\nu$ balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is $v < w$, the speed of the counter is $u < w$?
1. If the automaton and the counter are at rest, T.e. $v=u=0$, then the counter will register $N_0$, balls during the time $\Delta t$.
$$N_0 = \nu \Delta t$$
2. If the automaton is at rest ($v = 0$) and the counter is moving with speed $u$, the number of registered particles is
$$N_1 = \nu \frac{w-u}{w+v} \Delta t$$
3. When the automaton and the counter move, the number of particles during the time $\Delta t$ is defined as
$$N_2 = \nu \frac{w-u}{w-v} \Delta t$$
per unit of time
$$n = \nu \frac{w-u}{w-v}$$
$${ν}' = ν\frac{w − u}{w − v}$$