Relative Motion

1. Relative Motion

2. Point of View • A plane flies at a speed of 200. km/h relative to still air. There is an 80. km/h wind from the southwest (heading 45° north of east). • What direction should the plane head to go due north? • What is the speed of the plane relative to the ground?

3. We need an end velocity in the direction of due north. Assign E to x and N to y. The wind velocity and the plane velocity must add to get the result. Different Motion plane q result wind

4. Velocity by Components • The velocity of the wind can be described in the ground’s coordinates. • wx = (80 km/h) cos 45° = 57 km/h • wy = (80 km/h) sin 45° = 57 km/h • The velocity of the plane is also described compared to the ground. • px = p cos q • py = p sin q

5. Velocity Vector Sum • The plane’s motion compared to the ground is the sum of the wind velocity and plane velocity. • vx = wx + px = wx + p cos q • vy = wy + py = wy + p sin q • The plane should only go north, so vx = 0. • wx = - p cos q • 57 km/h = - (200. km/h) cos q • cos q = -0.285, or q = 106.6° ≈110° compared to +x axis

6. The speed of the plane can be measured from the ground. The velocity as measured from the ground was given. The angle was found. Finally the speed is found. Simplified since the plane is headed north compared to the ground. View from the Ground

7. Rest Frame • The ground had a special meaning to us. • We felt like we were the observers, and should be at rest. • The ground is our rest frame. • The plane and wind each also have a rest frame. • The laws of physics should look the same to all observers in a proper frame. next