Question

A hare and a tortoise compete in a race over a straight course 1.10 km long. The tortoise crawls at a speed of 0.150 m/s toward the finish line. The hare runs at a speed of 7.15 m/s toward the finish line for 0.880 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 7.15 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

Answer 1

Hint -always convert the given data into SI units before solving.

Total distance covered by the tortoise = 1.10 km = 1100 metres

speed of tortoise during the journey = .150 m/s

There fore time taken by tortoise to complete the race = Distance/speed

= 1100 / .150 =7333.33 seconds

Now we calculate the time taken by the hare to complete the race.

It can be divided into three parts =( time taken to complete first .880 km distance + time of rest + time taken to complete 1.10-.880 =.220 km distance )

time taken in first part = distance / speed = .880 km / 7.15 ms^-1

  =880 metres / 7.15 ms^-1

= 123.07 seconds

Time taken by hare to complete the remaining race = 220 metres / 7.15 ms^-1

= 30.77 seconds

Time of rest of hare = total time of journey - time of motion of hare

= 7333.33 - (123.07 + 30.77)

= 7333.33 - 153.84 = 7179.49 seconds.

distacnce covered by the tortoise while the hare was in rest and completed his first part of race

= speed of tortoise X (time taken by hare to complete first part of race + time of rest)

= .150 X (123.07 + 7179.49)

= .150 X 7302.56

= 1095.384 metres

Now remaining distance to be covered by tortoise = 1100 - 1095.384 = 4.616 metres this is the distance of tortoise from finishing line when the hare rejoins the race. A great story by the way .........

if in your answer sheet the answer is approximate then you can take the answer as 4.6 metres however the exact datas are given by me in the solution.