A hare and a tortoise compete in a race over a straight course 1.85 km long. The

Question

A hare and a tortoise compete in a race over a straight course 1.85 km long. The tortoise crawls at a speed of 0.230 m/s toward the finish line. The hare runs at a speed of 8.25 m/s toward the finish line for 1.480 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 8.25 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

Explanation / Answer

time for tortise to reach the finish line

t=d/v =1850/0.23

t=8043.5 sec

Time for hare to reach the finsih line

t=1480/8.25 =179.4 sec

Let the Hare takes rest for time T

Then for second trip

t=(1850-1480)/8.25 =44.85 sec

The total time of both hare and tortise are same

8043.5=179.4+T+44.9

T=7819.25 sec

The hare resumes the race after

t=(179.4+7819.25)=7998.65 sec

a)

Distance of tortise from finish line

d=1850-(0.23*7998.65)

d=10.3 m

b)

Wait time

t=7819.25 sec

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