Вдоль одной ступеньки движущегося эскалатора (поперёк направлению движения) туда и обратно бегает жук. Нарисуйте примерный вид траектории движения жука относительно земли. Объясните форму траектории.

The trajectory of the bug running back and forth across a single step of a moving escalator, as viewed relative to the ground, forms a unique pattern. This pattern emerges from the combination of two distinct motions: the bug's movement and the escalator's ascent.

As the escalator moves upwards, any point on it (including the bug, when it's not moving relative to the step) travels in a straight vertical line relative to the ground. However, the bug is also moving back and forth across the step. This back-and-forth movement is perpendicular to the escalator's upward motion.

When we combine these two movements, the resulting trajectory from the ground's perspective becomes a wave-like or looped path. Each horizontal movement of the bug (either to the left or right across the step) forms one half of a wave or loop. When the bug turns around and moves in the opposite direction, it completes the other half of the loop.

The reason for this wave-like pattern is that while the bug moves horizontally across the step, the escalator continues moving upwards. So, the bug's horizontal motion is superimposed onto the upward motion of the escalator. If the bug moves faster, the waves or loops become wider (more horizontal distance is covered), and if the escalator moves faster, the waves or loops become taller (more vertical distance is covered).

In conclusion, the combination of the bug's horizontal back-and-forth motion and the steady vertical ascent of the escalator results in the distinctive wavy or looped trajectory relative to the ground.