A hare and a tortoise compete in a race over a straight course 2.35 km long. The

Question

A hare and a tortoise compete in a race over a straight course 2.35 km long. The tortoise crawls at a speed of 0.120 m/s toward the finish line. The hare runs at a speed of 9.00 m/s toward the finish line for 1.880 km and then stops to tease the slow-moving tortoise as the tortoise eventually passes by. The hare waits for a while after the tortoise passes and then runs toward the finish line again at 9.00 m/s. Both the hare and the tortoise cross the finish line at the exact same instant. Assume both animals, when moving, move steadily at their respective speeds.

(a) How far is the tortoise from the finish line when the hare resumes the race? (answer in m)

(b) For how long in time was the hare stationary? (answer in s)

Explanation / Answer

The tortoise moves at a steady 0.12 m/s over a 2350 m course. That takes him 2350m/0.12m/s = 19583.3 seconds.

If the hare ran without stopping, it would take him 2350/9.0 = 261.1 seconds.

The difference should be the time the hare stopped or 19583.3 - 261.1 = 19322.2 seconds.

The hare runs at 9.0 m/s sec for 1.88 km, or 1880 m. That takes the hare 1880/9 = 208.9 seconds. The hare waits for 19322.2 seconds. That means that the hare has spent 208.9 + 19322.2 = 19531.1 seconds before he starts up again.

Since the tortoise streaks along at 0.12 m/s, he has traveled 0.12 m/s x 19531.1 sec = 2343.732 m when the hare starts up. That means he is 2350 - 2343.732 = 6.268 m from the finish line when the hare starts up.

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