A spaceship is moving in a straight line at a speed of 0.8 c (relative to Earth)

Question

A spaceship is moving in a straight line at a speed of 0.8 c (relative to Earth). It launches a that moves away from the spaceship (trawling in the same direction as the spaceship) at a speed of 0.6 c. Relative to Earth, the speed of the missile is (A) greater than 0.8 c and less than c. (B) c. (C) greater than c and less than 1.4 c. (D) 1.4 c. You are a passenger on a spaceship. As the speed of the spaceship increases, you would observe (A) your watch slowing down. (B) your watch speeding up. (C) nothing unusual about your watch. Which of the following results shows the validity of the relativistic effect of time dilation? (A) the detection of gravity waves (B) bending of light near the Sun (C) the decay of (D) red shift in distant galaxies A 30-year-old astronaut goes off on long term mission in a spacecraft that travels at 0.9 c. The mission last exactly 20 years as measured on Earth. Biologically speaking the astronaut's age would be (A) more than 50 years (B) exactly 50 years (C) more than 30 years and less than 50 years (D) exactly 30 years Observer A sees a ruler moving by in a relativistic train and measures its length to be L_A Observer B moves together with the train and measures the length of the ruler to be L_B These two results will be such that (A) L_A L_b (D) L_a could be greater of smaller than L_B depending on the direction of the motion

Explanation / Answer

Let S be the earth’s reference frame, and S’ be the reference frame of the spaceship. The spaceship travels at v = 0.8 c, and the rocket at u’ = 0.6 c. The question is to determine the speed of the rocket relative to earth, i.e., frame S. As we cannot apply the Galilean velocity addition, since it would violate the second postulate, 0.8 c + 0.6 c = 1.4 c, we apply the relativistic velocity transformation:
u = (u’ + v) / [1 + (u’v / c2)] = (0.6 c + 0.8 c) / [1 + (0.6 c) (0.8 c) / c2]

= 1.4 c / [1 + 0.48] = 1.4 / 1.48 = 0.95 c.

The answer will be (A).

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