Question

A hare and a tortoise compete in a race over a straight course 1.00 km long. The tortoise crawls at a speed of 0.200 m/s toward the finish line. The hare runs at a speed of 8.00 m/s toward the finish line for 0.800 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 8.00 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?

Answer 1

Answer:

a) 5 m from the finish line

b) 4875 s

Explanation:

distance = 1 km

tortoise speed = 0.2 m/s

speed of hare = 8 m/s

time take by hare t reach 0.8 km = $\dfrac{800}{8} = 100 s$

time taken by tortoise to travel 1 km = $\dfrac{1000}{0.2} = 5000s$

time taken by the hare to travel 0.2 km = $\dfrac{200}{8} = 25 s$

time taken by the tortoise to travel 0.2 km = $\dfrac{200}{0.2} = 500s$

distance traveled by tortoise in 25 second = 25 × 0.2 = 5 m

a) when tortoise is 5 m from the finish line then hare will resume the race.

b) the hare will be stationary for = 5000 - 125  = 4875 s