
Concept explainers
(a)
Speed of the spaceship in frame
(a)

Explanation of Solution
Given:
Spaceship that is at rest in frame
Spaceship is given further boost 2 of
Process is continued indefinitely at
Formula used:
Write the expression of equation for relativistic velocity addition
Here,
Simplify the above expression
Calculation:
Substitute 0 for
For rest of the values of
Number of boosts | Speed after |
2 | 0.800 |
3 | 0.929 |
4 | 0.976 |
5 | 0.992 |
6 | 0.997 |
7 | 0.999 |
8 | 1.000 |
9 | 1.000 |
10 | 1.000 |
Draw a diagram to plot the speed in units of
Conclusion:
Thus, the speed is calculated and represented graphically as a function of number of boosts.
(b)
Graphical representation of gamma factor.
(b)

Explanation of Solution
Given:
Spaceship that is at rest in frame
Spaceship is given further boost 2 of
Process is continued indefinitely at
Formula used:
Write the expression of gamma factor
Here,
Calculation:
Substitute 0 for
For rest of the values of
Number of boosts | Gamma factor after |
1 | 1.15 |
2 | 1.67 |
3 | 2.69 |
4 | 4.56 |
5 | 7.83 |
6 | 13.52 |
7 | 23.39 |
8 | 40.51 |
9 | 70.15 |
10 | 121.50 |
Draw a diagram to plot the gamma factor along
Conclusion:
Thus, the gamma factor is calculated and represented graphically as a function of number of boosts.
(c)
Number of required boosts until speed of ship in
(c)

Explanation of Solution
Introduction:
A spaceship that is at rest in frame
The graph of the speed after
Conclusion:
Thus, the number of required boosts until speed of ship in
(d)
Distance traveled by spaceship as well as average speed of spaceship between boost 1 and boost 6 in frame
(d)

Explanation of Solution
Given:
Spaceship that is at rest in frame
Spaceship is given further boost 2 of
Process is continued indefinitely at
Formula used:
Write the expression of distance traversed by spaceship between boosts 1 and 6 in frame
Write the expression for elapsed time between boosts 1 and 6 in frame
Write the expression for average speed of spaceship in frame
Calculation:
Substitute
Substitute
Conclusion:
Thus, the distance traveled by spaceship is
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Chapter 39 Solutions
Physics for Scientists and Engineers
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