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Exam 27: Relativity

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Question 41

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A person in a rocket ship traveling past the earth at a speed of 0.500c fires a laser gun in the forward direction. With what speed does an observer on Earth measure for the light pulse?

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Question 42

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A spaceship enters the solar system moving toward the sun at a constant speed relative to the sun. By its own clock, the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is 50.0 minutes. -As measured in the coordinate system of the sun, how long did it take for the spaceship to travel that distance? The radius of the orbit of Jupiter is 778 × 10⁹ m, and that of the orbit of Mars is 228 × 10⁹ m.

A) 30.0 minutes
B) 43.6 minutes
C) 58.6 minutes
D) 69.8 minutes
E) 95.8 minutes

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Question 43

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A spaceship with a constant speed of 0.800c relative to Earth travels to a star that is 4.30 light-years from Earth. How much time for this trip would elapse on a clock on board the spaceship?

The relativistic kinetic energy formula is valid

During a reaction, a reactant loses 4.8 × 10^-28 kg of mass. How many joules of energy are released? (c = 3.0 × 10⁸ m/s)

Two satellites with equal rest masses of 100 kg are traveling toward each other in deep space. They have identical speeds of 0.600c. The satellites collide and somehow manage to stick together. What is the rest mass of the combined object after the collision?

Suppose one twin takes a ride in a spaceship traveling at a very high speed to a distant star and then back again, while the other twin remains on Earth. Compared to the twin who remained on Earth, the astronaut twin is

Observer A sees a ruler moving by in a relativistic rocket and measures its length to be L_A. Observer B moves along with the rocket and measures the length of the ruler to be L_B. What is true about these two length measurements?

How fast would a rocket ship have to move past Earth to contract to half of its proper length as observed by an Earth-based physicist?

As measured in Earth's rest frame, a spaceship traveling at 0.9640c takes $10.5 \mathrm { y }$ to travel between two planets that are not moving relative to each other. How long does the trip take as measured by someone on the spaceship?

When a proton is traveling at 0.80c, what is the ratio of its kinetic energy to its rest energy?

As shown in the figure, the captain of spaceship A observes spaceship E escaping with a relative velocity of 0.35c. A missile M is fired from ship A directly toward ship E, with a velocity of 0.76c relative to ship A. What does the captain of ship E measure for the velocity of the missile M?

A satellite, initially at rest in deep space, separates into two pieces, which move away from each other. One piece has a rest mass of 190 kg and moves away with a speed 0.500c, and the second piece has a rest mass of 250 kg and moves in the opposite direction. What is the speed of the second piece?

How much energy would be released if 2.0 kg of material was lost during a reaction? (c = 3.0 × 10⁸ m/s)

Two stars are at rest relative to each other. In their common rest frame, these stars are 90.0 light-years apart. If they are measured to be $68.7 \text { light-years }$ apart by the navigator of a spaceship traveling between them, how fast is the spaceship moving relative to these stars?

A spaceship carrying a light clock moves at a speed of 0.960c relative to an observer on Earth. If the clock on the ship advances by 1.00 s as measured by the space travelers aboard the ship, how long did that advance take as measured by the observer on Earth?

If you were in a spaceship traveling close to the speed of light with respect to Earth, you would notice that

How fast (in terms of the speed of light)should a moving clock travel if it is to be observed by a stationary observer as running at one-half its normal rate?

A particle physicist observes cosmic rays creating a new particle high in the atmosphere, and the speed of this particle is measured at 99.7% the speed of light. It is unstable, and is observed to decay in an average 37.0 μs. If this particle were at rest in the laboratory, what would be its average lifetime?

A starship is constructed to be 100 m long in the factory. It is launched and as it coasts by Earth, it is measured to be shortened to 5.48 m long. (a)How fast, in terms of the speed of light, is it moving past Earth? (b)What length does the ship's crew measure for the ship?