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<blockquote data-quote="Ovinomancer" data-source="post: 7493797" data-attributes="member: 16814">Gah.&nbsp; Okay, once more unto the breach.NO CROSSWIND CASE:City frame -- car drives at 20 kph.&nbsp; Air resists.&nbsp; Force of the car's motor is exactly cancelled by the force of the air's resistance.&nbsp; Car's frame -- headwind blows at 20 kph.&nbsp; Car resists.&nbsp; Force of the wind's push is exactly cancelled by the force of the car's motor.CROSSWIND CASE:5 kph crosswind at 90 degrees to the path of the car.City frame -- car drives at 20 kph.&nbsp; Air resists.&nbsp; Force of the car's motor is exactly cancelled by the force of the air's resistance.&nbsp; Wind blows from left.&nbsp; Pushes car to right.&nbsp; Force of push exactly cancelled by tire friction.Car frame -- headwind blows at 20 kph.&nbsp; Car resists.&nbsp; Force of the wind's push is exactly cancelled by the force of the car's motor.&nbsp; Wind blows from left.&nbsp; Pushes car to right.&nbsp; Force of push exactly cancelled by tire friction.In both cases, the forces in the direction the car is pointing DO NOT CHANGE.&nbsp; In the crosswind case, there's a new force pushing the car to the right.&nbsp; This force doesn't change IN EITHER FRAME.What you're doing is saying that the headwind is part of the crosswind.&nbsp; It isn't.&nbsp; It exists exactly the same whether the crosswind exists or not.&nbsp; If the crosswind exists, it exists exactly the same in either frame.&nbsp; The vector of adding the headwind to the crosswind in the car frame DOES NOT MEAN THE WIND CHANGES DIRECTION.&nbsp; It means you can add them if you want, like all vectors.&nbsp; But the forces to the front of the car and to the side of the car do not change when you change the frame.&nbsp; The crosswind applies the exact same force to the side of the car in either frame.&nbsp; It doesn't change direction.Honestly, when I first saw this example, I was unexcited because of this exact problem -- the presence of air would lead to people making this exact mistake of conception with 'headwinds'.</blockquote>

[QUOTE="Ovinomancer, post: 7493797, member: 16814"] Gah. Okay, once more unto the breach. NO CROSSWIND CASE: City frame -- car drives at 20 kph. Air resists. Force of the car's motor is exactly cancelled by the force of the air's resistance. Car's frame -- headwind blows at 20 kph. Car resists. Force of the wind's push is exactly cancelled by the force of the car's motor. CROSSWIND CASE: 5 kph crosswind at 90 degrees to the path of the car. City frame -- car drives at 20 kph. Air resists. Force of the car's motor is exactly cancelled by the force of the air's resistance. Wind blows from left. Pushes car to right. Force of push exactly cancelled by tire friction. Car frame -- headwind blows at 20 kph. Car resists. Force of the wind's push is exactly cancelled by the force of the car's motor. Wind blows from left. Pushes car to right. Force of push exactly cancelled by tire friction. In both cases, the forces in the direction the car is pointing DO NOT CHANGE. In the crosswind case, there's a new force pushing the car to the right. This force doesn't change IN EITHER FRAME. What you're doing is saying that the headwind is part of the crosswind. It isn't. It exists exactly the same whether the crosswind exists or not. If the crosswind exists, it exists exactly the same in either frame. The vector of adding the headwind to the crosswind in the car frame DOES NOT MEAN THE WIND CHANGES DIRECTION. It means you can add them if you want, like all vectors. But the forces to the front of the car and to the side of the car do not change when you change the frame. The crosswind applies the exact same force to the side of the car in either frame. It doesn't change direction. Honestly, when I first saw this example, I was unexcited because of this exact problem -- the presence of air would lead to people making this exact mistake of conception with 'headwinds'. [/QUOTE]

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