## Task 1 - 020921

During the group flight of Soviet cosmonauts Andrian Nikolayev and Pavel Popovich, the spacecraft Vostok III and Vostok IV had a distance of only $6.5 \mathrm{~km}$ from each other. For simplicity, assume that they flew exactly one behind the other. They completed one orbit around the Earth ( $41000 \mathrm{~km}$ ) in about 88 minutes.

What distance would two cars traveling at a speed of $100 \frac{\mathrm{km}}{\mathrm{h}}$ on the highway need to have if their time difference was the same as that of the spacecraft?
The two spaceships have a speed of

$$
v=\frac{41000 \mathrm{~km}}{88 \mathrm{~min}} \cdot 60 \frac{\mathrm{min}}{\mathrm{h}} \approx 27955 \frac{\mathrm{km}}{\mathrm{h}}
$$

which results in a time difference of

$$
t_{\Delta}=\frac{6.5 \mathrm{~km}}{27955 \frac{\mathrm{km}}{\mathrm{h}}} \approx 0.0002325 \mathrm{~h}
$$

At a speed of $100 \frac{\mathrm{km}}{\mathrm{h}}$, this corresponds to a distance of $0.0002325 \mathrm{~h} \cdot 100 \frac{\mathrm{km}}{\mathrm{h}}=$ $0.02325 \mathrm{~km}=23.25 \mathrm{~m}$.