If a speed moves away from you at half the speed of light and fires a rocket away from you at half the speed of light relative to the spaceship, common sense may tell you the rocket moves at the speed of light relative to you. But it doesn’t! The relativistic addition of velocities is given by

$$V = \frac { v _ { 1 } + v _ { 2 } } { 1 + \frac { v _ { 1 } v _ { 2 } } { c ^ { 2 } } }$$

Substitute 0.5c for both

$$v_1$$

and

$$v_2$$

and show that the velocity V of the rocket relative to you is 0.8c.

How did the belief that the world should be viewed realistically manifest itself in science, art, and literature in the second half of the nineteenth century?

Find the distance between a and b. $a = 126, b = 75$

Find the slope of the line that passes through each pair of points. (-4, 7), (3, 5)

Identify the slope and y-intercept of the line with the given equation. y = 2x - 5

The path of light in a vertical “light clock” in a high-speed spaceship is seen to be longer when viewed from a stationary frame of reference. Why, then, does the light not appear to be moving faster?

¿Qué canta un enamorado a su amada? _ _ 2 3 _ _ _ _ _ _ _

The ratio of velocity gain to time for a freely falling body is g. Similarly, what is the ratio of distance to time for light waves?

Solve each proportion.

$$\frac { 9 } { 24 } = \frac { 12 } { n }$$

Simplify. Assume that variable exponents represent positive integers.

$$5 r ^ { 2 } \cdot r ^ { 4 }$$

If you were traveling in a high-speed spaceship, would meter sticks on board appear contracted to you? Defend your answer.

If you were in a smooth-riding train with no windows, could you sense the difference between uniform motion and rest? Between accelerated motion and rest? Explain how you could do this with a bowl filled with water.

Find the real roots of each equation by graphing. $x^{4}+3 x^{2}-2 x+5=0$

Does wave interference occur for waves in general, or only for light waves? Give examples to support your answer.