Tortoise vs Hare: Solve Homework Problem

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In summary, a tortoise and hare have a 1000-meter race with the tortoise moving at a constant speed of 2.30 cm/s and the hare initially moving at an average speed of 1.50 m/s for 10.0 minutes before taking a nap. After waking up, the hare accelerates with a constant acceleration of 0.500 m/s/s for the remaining distance. If the tortoise wins by a hair, the time in hours that the hare napped can be calculated as 11.9 hours by subtracting the times it took for the tortoise and hare without the nap.
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Prototype44
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Homework Statement


Help me with this particular problem.

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/s/s 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?

t for tortoise=50 000s t for hare without nap=620s

Homework Equations





The Attempt at a Solution


I get 13.7hr when the answer is 11.9hr subtracting those amounts.
 
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  • #2
How did you get that result?

ehild
 

1. What is the Tortoise vs Hare problem?

The Tortoise vs Hare problem is a mathematical problem that involves a race between a tortoise and a hare. The tortoise moves at a steady pace, while the hare moves at a variable speed. The question is, under what conditions will the hare and the tortoise tie in a race?

2. What is the origin of the Tortoise vs Hare problem?

The Tortoise vs Hare problem can be traced back to an ancient Greek fable by Aesop, called "The Tortoise and the Hare." In the fable, the tortoise and the hare compete in a race, and the tortoise ultimately wins by maintaining a steady pace while the hare becomes overconfident and takes a nap.

3. How do you solve the Tortoise vs Hare problem?

The most common way to solve the Tortoise vs Hare problem is by using algebraic equations and setting the distances traveled by both the tortoise and the hare equal to each other at the finish line. This allows for the determination of the conditions under which the animals will tie in the race.

4. What factors can affect the outcome of the Tortoise vs Hare problem?

The outcome of the Tortoise vs Hare problem can be affected by various factors such as the distance of the race, the initial distance between the tortoise and the hare, and the variable speed of the hare. These factors can change the conditions under which the animals will tie in the race.

5. How is the Tortoise vs Hare problem relevant in real life?

The Tortoise vs Hare problem is relevant in real life as it highlights the importance of consistency and perseverance. It also demonstrates the consequences of becoming overconfident and not taking into account all factors in a situation. This can be applied in various scenarios such as sports competitions, academic performance, and even daily life situations.

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