# The length of object when the velocity of the object is 0.5 c , 0.75 c and 0.9 c . ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.1, Problem 75E

(a)

To determine

## The length of object when the velocity of the object is 0.5c , 0.75c and 0.9c .

Expert Solution

The length of object when the velocity of the object is 0.5c , 0.75c and 0.9c are 8.66m , 6.61m and 4.34m .

### Explanation of Solution

Given:

The length of the object is a function of its velocity and the length of the object at rest is 10m .

The length of the object at velocity v is given by,

L(v)=101v2c2

Calculation:

The length of the object at velocity v is given by,

L(v)=101v2c2 (1)

Substitute 0.5c for v in equation (1) to find L(0.5c) ,

L(0.5c)=101(0.5c)2c2=1010.52=8.66m

Substitute 0.75c for v in equation (1) to find L(0.75c) ,

L(0.75c)=101(0.75c)2c2=1010.752=6.61m

Substitute 0.9c for v in equation (1) to find L(0.9c) ,

L(0.9c)=101(0.9c)2c2=1010.92=4.34m

Thus, the length of object when the velocity of the object is 0.5c , 0.75c and 0.9c are 8.66m , 6.61m and 4.34m .

(b)

To determine

### The variation of length of object according to the increase in velocity.

Expert Solution

The length of the object decreases as the velocity of object increases.

### Explanation of Solution

Given:

The length of the object is a function of its velocity and the length of the object at rest is 10m .

The length of the object at velocity v is given by,

L(v)=101v2c2

Calculation:

The length of the object at velocity v is given by,

L(v)=101v2c2

If the velocity of object increase then the term 1v2c2 decreases due to which the length decreases.

Thus, as the velocity increases the length of the object decreases.

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