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Two cyclists approach each other from opposite directions on a bike path. Amy is cycling east at 5.7 m/s, while Colin is cycling west at 6.4 m/s. Meanwhile, Carolyn is standing on the side of the path, watching all this happen. a) What is Colin's speed and direction, relative to Amy? b) What is Carolyn's speed and direction, relative to Colin?

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Borys Shumyatskiy eNotes educator | Certified Educator

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As we know, any mechanical movement of a physical body occurs only relative to some other body. The most common reference body on Earth's surface is Earth itself. We consider it "at rest," although this is relative, too.

So, "Amy is cycling East at `5.7` m/s, while Colin is cycling West at `6.4` m/s" means that they have these speeds and directions relative to Earth. "Carolyn is standing" means she is at rest relative to Earth.

All three persons move with constant velocities (speeds and directions) relative to each other. Relative to Amy, Colin's direction is towards her, the west direction, and the speed is the sum of their speeds relative to Earth, i.e. `5.7+6.4=12.1` (m/s). This is the answer for a).

Relative to Colin, Carolyn's speed is the same `6.4` m/s, and the direction is towards Colin, to the east. This is the answer for b).

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