Question

A hare and a tortoise compete in a race over a straight course 1.30 km long. The tortoise crawls at a speed of 0.300 m/s toward the finish line. The hare runs at a speed of 8.85 m/s toward the finish line for 1.040 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 8.85 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) How long was the hare stationary?

Answer 1

(b)

So the tortoise moves at a steady 0.3 m/s over a 1300m course. That takes him time

= 1300/0.3 = 4333.33 seconds.

If the hare ran without stopping, it would take him 1300/8.85 = 146.89 seconds.

The difference should be the time the hare stopped or 4333.33 – 146.89 = 4186.44seconds.

(a)

The hare runs at 8.85 m/s sec for 1040 m. That takes the hare 1040/8.85 = 117.51 seconds.

The hare waits for 4186.44 seconds. That means that the hare has spent 117.51 + 4186.44 = 4303.95 seconds before he starts up again.

Since the tortoise streaks along at 0.3 m/s, he has traveled 0.3 x 4303.95 = 1291.19m when the hare starts up.

That means he is 1300 – 1291.19 = 8.81 m from the finish line when the hare starts up.