Question on relative velocity (High school motion)

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Sue's rowing speed of 4.5 m/s is measured in still water, while the river's current flows at 2.5 m/s. When rowing against the current, her effective velocity relative to the land is 2 m/s, not 0.5 m/s backward as initially thought. The key is understanding that her rowing speed remains 4.5 m/s relative to the water, which is essential for calculating her overall motion. The analogy of a moving sidewalk illustrates how relative velocities work in different frames of reference.
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Homework Statement



Sue rows her boat at 4.5ms. The velocity of the river flow is 2.5ms. What is sues velocity against the flow relative to the water. I can't wrap my head around the question, since sues actual velocity against the flow is 2ms. This should mean she is moving backwards 0.5ms every 2ms she moves forwards right? Then how can the answer be sue distances 4.5ms from the waters perspective? I don't get it.[/B]

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The Attempt at a Solution

 
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It can help to draw a picture. Recognise that the 4.5 m/s is relative to still water. So, when Sue is rowing against a 2 m/s current (relative to the land), her net forward velocity is 2.5 m/s relative to the land.

Think of an analogy of a moving sidewalk that moves at 3 m/s. If you walk at 1 m/s (relative to still, ordinary floors) you will travel at 2m/s if you walk against the moving sidewalk and at 4 m/s if you walk with it.
 

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