A hare and a tortoise compete in a race over a straight course 1.05 km long. The

Question

A hare and a tortoise compete in a race over a straight course 1.05 km long. The tortoise crawls at a speed of 0.290 m/s toward the finish line. The hare runs at a speed of 7.95 m/s toward the finish line for 0.840 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 7.95 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?

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

Explanation / Answer

a)

total time before finish of race = 1050/0.29 = 3620.69 sec

the hare stops after = 840/7.95 = 105.66 sec

At that time, tortoise is 1050-0.29*105.66 = 1019.36m away from finish.

When hare resumes the race, the tortoise is = 1050-0.29(3488.615+105.6) = 7.678m

b)

remaining distance for hare = 210m

hare needs time = 210/7.95 = 26.415 sec

hare stays for = 3620.69-105.66-26.415 = 3488.615 sec

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