Question

ДАЮ ВСЕ СВОИ 30 БАЛОВ ПОМОГИТЕ!!! Реши задачу.Со схемой Автобус движется с постоянной скоростью 40 км/ч. С какой скоростью должно двигаться другое транспортное средство для того,чтобы скорость изменения расстояния между ними равнялась 60 км/ч? Найди два варианта ответа на этот вопрос: 1) при движении в одном и том же направлении,2) при движении в противоположных направлениях. Проиллюстрирую каждый вариант найденного ответа на движения из одной точки.

Answer 1

1 Вариант 

40+60=100 км/час Это если они движутся в одном направлении.

 

2 Вариант

 

Движутся в разных направлениях

 

60-40=20 км/час

Answer 2

40+60=100 км/ч - скорость второго тр. ср. при движении в одном направлении60-40=20 км/ч - скорость второго тр. ср. при движении в противоположных направлениях

Answer 3

Problem Analysis

We are given that a bus is moving at a constant speed of 40 km/h. We need to find the speed at which another vehicle should move in order for the rate of change of the distance between them to be 60 km/h. We need to find two scenarios: one where the vehicles are moving in the same direction and another where they are moving in opposite directions.

Same Direction

When the vehicles are moving in the same direction, the relative speed between them is the difference of their individual speeds. Let's assume the speed of the other vehicle is v km/h.

The rate of change of the distance between the vehicles is the difference between their speeds, which is 60 km/h. Therefore, we can set up the equation:

40 km/h - v km/h = 60 km/h

Simplifying the equation, we get:

v km/h = 40 km/h - 60 km/h

v km/h = -20 km/h

The negative sign indicates that the other vehicle should be moving in the opposite direction at a speed of 20 km/h.

Opposite Direction

When the vehicles are moving in opposite directions, the relative speed between them is the sum of their individual speeds. Let's assume the speed of the other vehicle is v km/h.

The rate of change of the distance between the vehicles is the sum of their speeds, which is 60 km/h. Therefore, we can set up the equation:

40 km/h + v km/h = 60 km/h

Simplifying the equation, we get:

v km/h = 60 km/h - 40 km/h

v km/h = 20 km/h

Therefore, the other vehicle should be moving in the opposite direction at a speed of 20 km/h.

Illustration

To illustrate the two scenarios, let's consider a point A as the starting position of the bus. We will assume that the bus is moving to the right. We will also assume that the other vehicle starts at point B, which is initially 100 km away from point A.

1. Same Direction: When the vehicles are moving in the same direction, the other vehicle should be moving to the left at a speed of 20 km/h. After 1 hour, the bus will be at point C, 40 km away from point A, and the other vehicle will be at point D, 20 km away from point A. The distance between them will be 20 km.

   A ----> C (40 km)
   B ----> D (20 km)
   

2. Opposite Direction: When the vehicles are moving in opposite directions, the other vehicle should be moving to the left at a speed of 20 km/h. After 1 hour, the bus will be at point C, 40 km away from point A, and the other vehicle will be at point E, 60 km away from point A. The distance between them will be 20 km.

   A ----> C (40 km)
   B <---- E (60 km)
   

Please note that the distances mentioned in the illustrations are for explanatory purposes and may not be to scale.

I hope this helps! Let me know if you have any further questions.