Three swimmers can swim equally fast relative to the water. They have a race to

Question

Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across a river in the least time. Swimmer A swims perpendicular to the current and lands on the far shore downstream, because the current has swept him in that direction. Swimmer B swims upstream at an angle to the current and lands on the far shore directly opposite the starting point. Swimmer C swims downstream at an angle to the current in an attempt to take advantage of the current. Who crosses the river in the least time?

Question is from the following text book: Physics - Cutnell 8th Edition. Chapter 3 under the Relative Velocity Section. The is a "Check Your Understanding" section following the chapter, question number 17.

Explanation / Answer

The time required for any given swimmer to cross the river is equal to the width of the river divided by the magnitude of the component of the velocity that is parallel to the width of the river. All three swimmers can swim equally fast relative to the water; however, all three swim at different angles relative to the current. Since swimmer A heads straight across the width of the river, swimmer A will have the largest velocity component parallel to the width of the river; therefore, swimmer A crosses the river in the least time.

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