Question

Колона вояків довжиною 400м рухається зі швидкістю 5км\год, велосипедист із хвоста колони з постійною швидкістю 25кмм\год їде до голови колони і назад, через скільки часу велосипедист повернеться до швоста колони

Answer 1

Систему отсчета свяжем с колонной.
Скорость колонны v = 0
Скорость велосипедиста v1 = 25 - 5 = 20 км/ч
t = 2*L / v1 = 2* 0,400 км / 20 км/ч = 0,800 / 20 = 0,04 ч = 2,4 мин

Answer 2

Problem Analysis

We have a column of soldiers moving at a speed of 5 km/h, and a cyclist traveling from the tail of the column to the head and back at a constant speed of 25 km/h. We need to determine how much time it will take for the cyclist to return to the tail of the column.

Solution

To solve this problem, we need to consider the relative speeds of the column and the cyclist. Let's break down the problem into two parts: the time it takes for the cyclist to reach the head of the column and the time it takes for the cyclist to return to the tail of the column.

1. Time to reach the head of the column: - The cyclist is traveling at a speed of 25 km/h. - The column is moving at a speed of 5 km/h. - The relative speed of the cyclist with respect to the column is the difference between their speeds: 25 km/h - 5 km/h = 20 km/h. - The distance the cyclist needs to cover to reach the head of the column is 400 m. - We can use the formula `time = distance / speed` to calculate the time it takes for the cyclist to reach the head of the column. - Plugging in the values, we get `time = 400 m / (20 km/h)`. - We need to convert the distance from meters to kilometers and the speed from kilometers per hour to meters per hour to ensure consistent units. - 400 m is equal to 0.4 km, and 20 km/h is equal to 20,000 m/h. - Substituting the values, we get `time = 0.4 km / (20,000 m/h)`. - Simplifying the units, we get `time = 0.4 km / (20,000/1,000) h`. - Dividing 0.4 km by 20,000/1,000, we get `time = 0.4 km / 20 h`. - The units cancel out, and we are left with `time = 0.4 / 20 h`. - Evaluating the expression, we find that it takes 0.02 hours for the cyclist to reach the head of the column.

2. Time to return to the tail of the column: - The cyclist is traveling at a speed of 25 km/h. - The column is moving at a speed of 5 km/h. - The relative speed of the cyclist with respect to the column is the difference between their speeds: 25 km/h - 5 km/h = 20 km/h. - The distance the cyclist needs to cover to return to the tail of the column is also 400 m. - Using the same formula `time = distance / speed`, we can calculate the time it takes for the cyclist to return to the tail of the column. - Plugging in the values, we get `time = 400 m / (20 km/h)`. - Following the same steps as before, we find that it takes 0.02 hours for the cyclist to return to the tail of the column.

Answer

Therefore, the cyclist will return to the tail of the column after approximately 0.02 hours.