A hare and a tortoise compete in a race over a straight course 1.80 km long. The

Question

A hare and a tortoise compete in a race over a straight course 1.80 km long. The tortoise crawls at a speed of 0.190 m/s toward the finish line. The hare runs at a speed of 7.55 m/s toward the finish line for 1.440 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 7.55 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?

Explanation / Answer

he distance must be such that the time for the tortoise to cover it is the same as the time it would take the hare to cover 0.200km. Here's how it is solved: ................Vi?8.0m/sec ........ /|¯¯|?°__________|t = 25secs ¦¦¦¦¦¦¦|¦¦¦¦¦¦¦¦|¦¦¦¦HARE ................|?-0.200km-?| S = vt (0.200 x 1000) = 8t t = 25 secs. (the time that it takes the hare to cover 0.200km) The tortoise can cover only this distance in 25 secs ............Vi?.200m/s .........../?//°__________|t = 25secs ¦¦¦¦¦¦¦|¦¦¦¦¦¦¦¦|¦¦¦¦TORTOISE ................|?---S = ?---?| S = vt ...= (0.200)(25) ...= 5m So, if the tortoise gets to be less than 5 meters from the finish line before the hare resumes running, the tortoise wins.

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