# Relative velocity

##### Intros

###### Lessons

##### Examples

###### Lessons

**Relative velocity in one dimension**

A car travelling at 75.0 km/h overtakes a 1.20 km long train travelling in the same direction on a track parallel to the road. The train moves at 60.0 km/h.

- How long does it take the car to pass and how far will it have travelled in this time?
- Find the time to pass and distance the car travels if the car and train move in opposite directions.

**Relative velocity in two dimensions**A pilot must fly her plane due west to an airport. The plane has a speed of 445 km/h relative to the air. There is a steady wind blowing 82.5 km/h toward the south.

- Draw a vector diagram.

- What is the heading of the plane relative to the ground that the pilot should fly? Why is it not due [W]?
- What is the speed of the plane relative to the ground?
- If the airport is 312 km west, how much time does she need to arrive there?

- Draw a vector diagram.
A boat heads across a 593 m wide river with a velocity of 3.50 m/s toward the east. The river current is flowing south. The boat lands 346 m downstream on the other side of the river.

- Draw a vector diagram for the boat's resultant velocity
- What is the speed of the river current?
- What is the velocity of the boat relative to the shore?

- What is the change in velocity of a ball that had an initial velocity of 16.5 m/s [S] and a final velocity of 20.8 m/s [E] after it is hit with a bat? Draw a vector diagram.

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###### Topic Notes

In this lesson, we will learn:

- How to solve relative velocity problems in one dimension
- How to solve relative velocity problems in two dimensions

__Notes:____Frame of reference__can be thought of as the point of view that measurements are made from.- A
__relative velocity__is a velocity that is measured in a frame of reference. Usually, a moving object is the frame of reference. - Imagine you are on a train leaving a station at 10 m/s [E]. A bystander at the station would see the train move at 10 m/s [E]: this is the velocity of the train relative to the station ( $\vec{v}_{train\,to\,station}$ ). The frame of reference is the station, since that is what the velocity is measured from.
- If you imagine yourself looking out the window of the train it might appear that the station is moving 10 m/s [W], even though you know that it is the train that is moving. This is the velocity of the station relative to the train ( $\vec{v}_{train\,to\,station}$ ) and the frame of reference is the train.

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