Question

По перрону идет человек со скоростью 5,4 км/час. В это время поезд длинной 540 метров. двигающейся в противоположном направлении, проходит мимо человека за 45 с. Определите скорость поезда.

Answer 1

Problem Analysis

We are given the following information: - A person is walking on a platform with a speed of 5.4 km/h. - At the same time, a train of length 540 meters is passing by the person in the opposite direction, taking 45 seconds to pass.

We need to determine the speed of the train.

Solution

To solve this problem, we can use the formula:

Relative Speed = Speed of the Person + Speed of the Train

The relative speed is the combined speed of the person and the train, as observed by an external observer.

Let's calculate the relative speed using the given information:

Speed of the Person = 5.4 km/h

Since the speed of the person is given in kilometers per hour, we need to convert it to meters per second to match the units of the train's speed.

Speed of the Person = 5.4 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 1.5 m/s

Now, let's calculate the speed of the train using the formula:

Relative Speed = Speed of the Person + Speed of the Train

Speed of the Train = Relative Speed - Speed of the Person

The train takes 45 seconds to pass the person, and its length is 540 meters. Therefore, the relative speed can be calculated as:

Relative Speed = Distance / Time = 540 m / 45 s = 12 m/s

Now, substituting the values into the formula, we can find the speed of the train:

Speed of the Train = 12 m/s - 1.5 m/s = 10.5 m/s

Therefore, the speed of the train is 10.5 m/s.

Answer

The speed of the train is 10.5 m/s.