   Chapter 2, Problem 14P

Chapter
Section
Textbook Problem

A tortoise can run with a speed of 0.10 m/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2.0 minutes. The tortoise wins by a shell (20 cm). (a) How long does the race take? (b) What is the length of the race?

(a)

To determine
The time taken for the race.

Explanation

Given Info:

The speed of tortoise is 0.10m/s .

The time the hare took rest is 2.0min .

The extra distance covered by tortoise is 20cm .

Explanation:

Formula used to calculate distance covered by the tortoise is,

xt=vtt (I)

• xt is the distance covered by the tortoise
• vt is the velocity of the tortoise
• t is the time taken for the tortoise to complete the race.

Formula used to calculate the velocity of the hare is,

vh=20vt

• vh is the velocity of the hare

Formula used to calculate the time taken by the hare is,

th=ttr

• th is the time taken for the hare
• tr is the time the hare took rest.

Formula used to calculate the distance covered by the tortoise is,

xt=xh+xs

• xh is the distance covered by the hare
• xh is the extra distance covered by tortoise.

Formula used to calculate distance covered by the hare is,

xh=vhth

Substitute vhth for xh to calculating xt .

xt=vhth+xs

Substitute ttr for th and 20vt for vh to calculating xt

(b)

To determine
The length of the race.

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