Two cars move evenly along the highway towards each other. Modules of their speeds are equal to 36 km

| September 11, 2021 | education

Two cars move evenly along the highway towards each other. Modules of their speeds are equal to 36 km / h and 20 m / s. Find the speed of the first car relative to the second and the second relative to the first.

V1 = 36 km / h.

V2 = 20 km / h.

V12 -?

V21 -?

According to the law of relativity of velocities, the speed of a body relative to a stationary frame of reference Vн is the vector sum of the speed of a moving frame of reference relative to a stationary Vпн and the speed of a body relative to a moving frame of reference Vп: Vн = Vпн + Vп.

1) The fixed frame of reference is the earth, the movable frame of reference is the second car.

Therefore, the speed of the second car relative to the ground V2 is the speed of the moving frame of reference Vнп: Vнп = V2.

The speed of the first car relative to the second V12 is the speed of the body relative to the moving frame of reference Vп: Vп = V12.

The speed of the first car relative to the ground V1 is the speed of the body relative to the stationary frame of reference Vн: Vн = V1.

V1 = V2 + V12 – vector.

For projections on the OX axis, directed towards the movement of the first car, the formula will take the form: V1 = – V2 + V12.

V12 = V1 + V2.

V12 = 36 km / h + 20 km / h = 56 km / h.

2) The fixed frame of reference is the earth, the movable frame of reference is the first car.

Therefore, the speed of the first car relative to the ground V1 is the speed of the moving frame of reference Vнп: Vнп = V1.

The speed of movement of the second car relative to the first V21 is the speed of the body, relative to the moving frame of reference Vп: Vп = V21.

The speed of the second car relative to the ground V2 is the speed of the body relative to the stationary frame of reference Vн: Vн = V2.

V2 = V1 + V21 – vector.

For projections onto the same OX axis: – V2 = V1 – V21.

V21 = V1 + V2.

V21 = 36 km / h + 20 km / h = 56 km / h.

The speed of the second car relative to the first will be directed in the opposite direction of the first car.

Answer: V12 = V21 = 56 km / h.



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