5. Two cars are driving towards a single intersection on two mutually perpendicular roads at constant speeds. At the initial moment, the first car was at a distance of $s_{1}=500 \mathrm{M}$ from the intersection, and for the second car, the analogous distance was $S_{2}=700 \mathrm{M}$. The speed of the first car is $v_{1}=36 \mathrm{kn} / \mathrm{h}$. At the moment when the first car arrived at the intersection, the distance between the cars was $s=100 \mathrm{m}$. Determine the speed of the second car. (15 points)
Answer: $12 \mathrm{~m} / \mathrm{c}$ or $16 \mathrm{~m} / \mathrm{c}$

## Solution.

The time of the first car's movement to the intersection $\quad t_{1}=\frac{s_{1}}{v_{1}}=\frac{500}{10}=50 \mathrm{c} . \quad$ (3 points) There are two possible scenarios. The second car has already passed the intersection or has not yet reached it. Therefore, the distance it has traveled:

$l_{1}=s_{2}-s=700-100=600 \mathrm{M}$ (3 points) or $l_{2}=s_{2}+s=700+100=800 \mathrm{M}$.

As a result, the speed of the second car: $\quad v_{2}=\frac{l_{1}}{t_{1}}=\frac{600}{50}=12 \mathrm{~m} / \mathrm{c}$

or $\quad v_{2}=\frac{l_{2}}{t_{1}}=\frac{800}{50}=16 \mathrm{~m} / \mathrm{c} \quad(3$ points $)$.