Relative Velocity using a Boat crossing a River



A boat points straight across the river, but due to the rivers speed the boat travels both across and down stream. The small diagram below shows the velocity of the boat relative to the shore (red arrow) as the vector sum of the rivers velocity relative to the shore (horizontal arrow) and the boats velocity relative to the river (vertical arrow).






In order for a boat to travel straight across the river without moving down stream, the boat must point at some angle up stream. By doing this, the boat has a component of its velocity pointing upstream. If that component is the same magnitude as the rivers downstream velocity, the two velocties cancel and the boat will travel straight across the river. The small diagram below shows the velocity of the boat relative to the shore (red arrow) as the vector sum of the rivers velocity relative to the shore (horizontal arrow) and the boats velocity relative to the river (angled arrow).




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