Question

A tortoise and a hare are having a 1000-meter race. the tortoise runs the race at a constant speed of 2.30 cm/s. the hare moves at an average speed of 1.50 m/s for 10.0 minutes and then decides to take a nap. after waking up from the nap, the hare recognizes that the tortoise is about to cross the finish line and immediately accelerates from rest with a constant acceleration of 0.500 m/s2 for the remaining distance of the race. if the tortoise wins by a hair (no pun intended), then what is the time in hours that the hare napped?

Answer 1

Tt = 1000 / .023 = 43,500 sec = 725 hrs time for tortoise to run race

H1 = 1.5 m/s * 600 s = 900 m distance traveled by hare in 10 min

H2 = 100 m = 1/2 a t^2 to get time traveled by hare for 100 m

t2 = (200 / .5)^1/2 = 20 sec time for hare to run last 100 m

Total time hare runs = (1/6 + 1/180) = 31 / 180 hrs

Time hare napped = 725 - .172 = 724.8 hrs or about 725 hrs