Relative Motion

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?

Different Motion 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. plane q result wind

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 as if in still air. px = p cos q py = p sin q

Velocity Vector Sum The plane’s net 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

View from the Ground The relative velocity in air was given. The angle was found. Finally the ground speed is found. Simplified since the plane is headed north compared to the ground. plane q result wind

Reference Frame Displacement is different from position The displacement is measured relative to the object’s current position. Velocity can be measured relative to the object’s current velocity. This is the relative velocity. Example: walking on a moving train. Some measurements may be taken in different reference frames. From the example: ground, plane, wind