BuyFind

Precalculus: Mathematics for Calcu...

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

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

Answer to Problem 75E

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

Answer to Problem 75E

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.

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!