# Problem №4 (15 points)

A train entered a railway bridge 1400 m long at a speed of 54 km/h. A person is walking through the train in the direction opposite to the train's movement at a speed of 3.6 km/h. The length of one carriage is $23 m$. In which carriage will the person be when the train leaves the bridge? At the moment the train enters the bridge, the person is in the first carriage.
# Solution:

Convert the initial data to the SI system:
$54 \kappa m / h = 15 \mu / s$

$3.6 \kappa m / h = 1 m / s$

The speed of the person relative to the ground:

$v_{\varphi} = 15 - 1 = 14 m / s$

(4 points)

This means the person will be on the bridge for:

$t = \frac{1400}{14} = 100 s$

During this time, he will walk along the train:

$S = v t = 1 \cdot 100 = 100 m$,

(2 points)

which corresponds to $\frac{100}{23} \approx 4.35$ carriages.

(2 points)

Since it is unknown in which part of the first carriage he was initially, by the time he leaves the bridge, the person will be in either the fifth or sixth carriage (5 points)

# Multidisciplinary Engineering Olympiad "Star"  NATURAL SCIENCES  2016 

March 29, 2016

PROTOCOL No. 1 of the Jury Meeting

PRESENT: Keller A.V., Zalyapin V.I., Zamishlyayeva A.A., Vorontsov A.G., Kuts D.A., Gusev A.V.

HEARD: about the distribution of points among the winners and prizewinners of the olympiad

## 11th Grade

- to consider the winners of the olympiad and award diplomas of the 1st degree to participants who scored 100 - 90 points;
- to consider the prizewinners of the olympiad and award diplomas of the 2nd degree to participants who scored 89 - 70 points;
- to consider the prizewinners of the olympiad and award diplomas of the 3rd degree to participants who scored 69 - 45 points.

## 10th Grade

- to consider the winners of the olympiad and award diplomas of the 1st degree to participants who scored 100 - 95 points;
- to consider the prizewinners of the olympiad and award diplomas of the 2nd degree to participants who scored 94 - 70 points;
- to consider the prizewinners of the olympiad and award diplomas of the 3rd degree to participants who scored 69 - 40 points.

## 9th Grade

- to consider the winners of the olympiad and award diplomas of the 1st degree to participants who scored 100 - 90 points;
- to consider the prizewinners of the olympiad and award diplomas of the 2nd degree to participants who scored 89 - 70 points;
- to consider the prizewinners of the olympiad and award diplomas of the 3rd degree to participants who scored 69 - 40 points.

## 8th Grade

- to consider the winners of the olympiad and award diplomas of the 1st degree to participants who scored 100 - 75 points;
- to consider the prizewinners of the olympiad and award diplomas of the 2nd degree to participants who scored 74 - 65 points;
- to consider the prizewinners of the olympiad and award diplomas of the 3rd degree to participants who scored 64 - 40 points.

## 7th Grade

- to consider the winners of the olympiad and award diplomas of the 1st degree to participants who scored 100 - 90 points;
- to consider the prizewinners of the olympiad and award diplomas of the 2nd degree to participants who scored 89 - 70 points;
- to consider the prizewinners of the olympiad and award diplomas of the 3rd degree to participants who scored 69 - 40 points.

## 6th Grade

- to consider the winners of the olympiad and award diplomas of the 1st degree to participants who scored 100 - 90 points;
- to consider the prizewinners of the olympiad and award diplomas of the 2nd degree to participants who scored 89 - 80 points;
- to consider the prizewinners of the olympiad and award diplomas of the 3rd degree to participants who scored 79 - 40 points.

## Chairmen of the Jury:

![](https://cdn.mathpix.com/cropped/2024_05_06_65636c5c9319cd549e45g-8.jpg?height=257&width=582&top_left_y=1096&top_left_x=180)

Keller A.V.

Vorontsov A.G.