# Relative velocity

### Relative velocity

#### Lessons

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.
• Introduction
Introduction to relative velocity
a)
Understanding the definitions of relative velocity

b)
The "observer" method for calculating relative velocities in one dimension

c)
The "observer" method for calculating relative velocities in two dimensions

• 1.
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.
1. How long does it take the car to pass and how far will it have travelled in this time?
2. Find the time to pass and distance the car travels if the car and train move in opposite directions.

• 2.
Relative velocity in two dimensions
a)

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.

1. Draw a vector diagram.
2. What is the heading of the plane relative to the ground that the pilot should fly? Why is it not due [W]?
3. What is the speed of the plane relative to the ground?
4. If the airport is 312 km west, how much time does she need to arrive there?

b)

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.

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

c)
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.