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A runner moves along a straight horizontal track while a wind blows with constant velocity perpendicular to the track. At the instant the runner starts, he perceives the wind blowing at 45 deg to the track (i.e., the relative velocity of wind with respect to the runner makes 45 deg with the track). By the finish line, the wind direction as perceived by the runner has rotated through a further 45 deg (now appearing parallel to the track, i.e., head-on or tail-on). Which of the following describes the runner's motion?

1. The runner is slowing down throughout the race
2. The runner is speeding up throughout the race
3. The runner comes to rest exactly at the finish line
4. The runner is still moving when he crosses the finish line

Correct answer: The runner is still moving when he crosses the finish line

Solution

Initially the runner has speed equal to the wind speed (angle = 45 deg). As the race progresses the perceived wind rotates toward 90 deg (perpendicular, meaning tail-component = runner speed approaches zero). So the runner decelerates from speed w to 0, reaching zero speed at the finish. But the question says he completes the race, implying he just barely reaches it.

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