   Chapter 2, Problem 69AP

Chapter
Section
Textbook Problem

One of Aesop’s fables tells of a rare between a tortoise and a hare. Suppose the overconfident hare takes a nap and wakes up to find the tortoise a distance d ahead and a distance L from the finish line. If the hare then begins running with constant speed v1 and the tortoise continues crawling with constant speed v2, it turns out that the tortoise wins the race if the distance L is less than (v2/(v1 − v2))d. Obtain this result by first writing expressions for the times taken by the hare and the tortoise to finish the nice, and then noticing that to win, ttortoise < thare. Assume v2 < v1.

To determine
Determine the condition at which the tortoise wins the game.

Explanation

The formula used to calculate the time taken by the hare to complete the race is,

thare=L+dv1

• thare is the time taken by the hare to complete the race
• L is the distance of the finishing line from the first stop of the hare
• d is the distance covered by the hare till the stop
• v1 is velocity of the hare

The formula used to calculate the time taken by the tortoise to complete the race is,

ttortoise=Lv2

• ttortoise is the time taken by the tortoise to complete the race
• v2

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