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A hare and a tortoise compete in a race over a straight course 2.10 km long. The tortoise crawls at a speed of 0.180 m/s toward the finish line. The hare runs at a speed of 8.70 m/s toward the finish line for 1.680 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 8.70 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?

?m

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

s?

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a)for hare:

time taken by hare for first 1.68 km

t =1.68 x 1000 / 8.7 =193.10 sec

to complete running time = 2.10 x1000 / 8.7 =241.38 sec

for tortoise :

time taken by tottoise = 1.68 x 1000 / 0.180 = 9333.33 sec

to complete = 2.10 x1000 / 0.18 = 11666.67 sec

time taken to complete last 2.10- 1.68 = 0.42 km

= 0.42 x1000 / 8.7 = 48.28 sec

so hare resumes 11666.67 - 48..28 sec = 11618.39 sec

d =ut = 0.180 x 11618.39 = 2091.31 m

or 2.09 km

b) so hare slept for = time taken by tortoise - by hare

= 11667.67 - 241.38 = 11426.29 sec

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