Relative velocity
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- 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 ( vtraintostation ). 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 ( vtraintostation ) and the frame of reference is the train.
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