Relative MotionPoint of ViewDifferent MotionVelocity by ComponentsVelocity Vector SumView from the GroundRest FrameReference FrameRelative MotionRelative MotionPoint of ViewPoint of ViewA plane flies at a speed of 200. km/h relative to still A plane flies at a speed of 200. km/h relative to still air. There is an 80. km/h wind from the southwest air. There is an 80. km/h wind from the southwest (heading 45(heading 45°° north of east). north of east).•What direction should the plane head to go due north?What direction should the plane head to go due north?•What is the speed of the plane relative to the ground?What is the speed of the plane relative to the ground?Different MotionDifferent MotionWe need an end velocity in We need an end velocity in the direction of due north.the direction of due north.•Assign E to Assign E to xx and N to and N to yy..The wind velocity and the The wind velocity and the plane velocity must add to plane velocity must add to get the result.get the result.resultplanewindVelocity by ComponentsVelocity by ComponentsThe velocity of the wind can be described in the The velocity of the wind can be described in the ground’s coordinates.ground’s coordinates.•wwxx = (80. km/h) cos 45 = (80. km/h) cos 45°° = 57 km/h = 57 km/h•wwyy = (80. km/h) sin 45 = (80. km/h) sin 45°° = 57 km/h = 57 km/hThe velocity of the plane is also described compared The velocity of the plane is also described compared to the ground as if in still air.to the ground as if in still air.•ppxx = = pp cos cos •ppyy = = pp sin sin Velocity Vector SumVelocity Vector SumThe plane’s net motion compared to the ground is the The plane’s net motion compared to the ground is the sum of the wind velocity and plane velocity.sum of the wind velocity and plane velocity.•vvxx = w = wxx + p + pxx = w = wxx + + pp cos cos •vvyy = w = wyy + p + pyy = w = wyy + + pp sin sin The plane should only go north, so vThe plane should only go north, so vxx = 0. = 0.•wwxx = - = - pp cos cos •57 km/h = - (200. km/h) cos 57 km/h = - (200. km/h) cos cos cos = = -0.285, or -0.285, or = = 106.6° ≈106.6° ≈ 110° compared to +x axis110° compared to +x axisView from the GroundView from the GroundThe speed of the plane can The speed of the plane can be measured from the be measured from the ground.ground.The velocity as measured The velocity as measured from the ground was given.from the ground was given.The angle was found.The angle was found.Finally the speed is found.Finally the speed is found.•Simplified since the plane is Simplified since the plane is headed north compared to headed north compared to the ground.the ground.km/h 250)sin()sin()cos(22vpwvpwpwvyyxRest FrameRest FrameThe ground had a special meaning to us.The ground had a special meaning to us.We felt like we were the observers, and should be at We felt like we were the observers, and should be at rest.rest.The ground is our rest frame.The ground is our rest frame.The plane and wind each also have a rest frame.The plane and wind each also have a rest frame.The laws of physics should look the same to all The laws of physics should look the same to all observers in a proper frame.observers in a proper frame.Reference FrameReference FrameDisplacement is different from positionDisplacement is different from position•The displacement is measured relative to the object’s The displacement is measured relative to the object’s current position.current position.Velocity can be measured relative to the object’s Velocity can be measured relative to the object’s current velocity.current velocity.•This is the relative velocity.This is the relative velocity.•Example: walking on a moving train.Example: walking on a moving train.Some measurements may be taken in an object’s Some measurements may be taken in an object’s reference framereference
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