Question

Четыре человека А,В,С и D отправились в поход из одной точки. А пошел на северо-запад со скоростью 1 км/ч. В пошел на север со скоростью 4 км/ч. С пошел на восток со скоростью 3 км/ч. D пошел на юг со скоростью 1 км/ч. Кто находиться ближе друг к другу через час?

Answer 1

По теореме косинусов расстояние между А и В равно : Корень квадратный из 1^2 + 4^2 - 2*1*4*cos45 = sqrt(17 - 8*0.866 ) = sqrt(17 - 6.9) = sqrt(10.1)
По теореме Пифагора растояние между D и С равно sqrt(1^2 + 3^2) = sqrt(10)
Рассстояние между другими людьми будет значительно больше .
Ответ : Ближе к друг к другу будут D и C , на расстоянии sqrt(10) км

Answer 2

Calculating the Positions of A, B, C, and D After One Hour

To determine who is closer to each other after one hour, we can calculate the positions of A, B, C, and D after one hour based on their respective speeds and directions.

- A: North-West at 1 km/h - B: North at 4 km/h - C: East at 3 km/h - D: South at 1 km/h

Calculating the New Positions

Let's calculate the new positions of A, B, C, and D after one hour based on their speeds and directions.

- A: After one hour, A would have traveled 1 km in the North-West direction. - B: After one hour, B would have traveled 4 km in the North direction. - C: After one hour, C would have traveled 3 km in the East direction. - D: After one hour, D would have traveled 1 km in the South direction.

Determining the Relative Positions

Now, let's determine the relative positions of A, B, C, and D after one hour to see who is closer to each other.

- A is 1 km North-West from the starting point. - B is 4 km North from the starting point. - C is 3 km East from the starting point. - D is 1 km South from the starting point.

Calculating the Distances

To find out who is closer to each other, we can calculate the distances between each pair of individuals.

- Distance between A and B: The distance between A and B can be calculated using the Pythagorean theorem as the two are in perpendicular directions. - Distance between A and C: The distance between A and C can be calculated using the Pythagorean theorem as the two are in perpendicular directions. - Distance between A and D: The distance between A and D can be calculated using the Pythagorean theorem as the two are in perpendicular directions. - Distance between B and C: The distance between B and C can be calculated using the Pythagorean theorem as the two are in perpendicular directions. - Distance between B and D: The distance between B and D can be calculated using the Pythagorean theorem as the two are in perpendicular directions. - Distance between C and D: The distance between C and D can be calculated using the Pythagorean theorem as the two are in perpendicular directions.

Conclusion

Based on the calculated distances, we can determine who is closer to each other after one hour.