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1.Suppose you are driving your car on a business trip and are traveling at 30 m/s. Your boss, who is waiting at your destination, expects the trip to take 5.0 h. When you arrive late, your excuse is that your car clock registered the passage of 5.0 h but that you were driving fast and so your clock ran more slowly than your boss’s clock. If your car clock actually did indicate a 5.0-h trip, how much time passed on your boss’s clock, which was at rest on the Earth?
2.Suppose you’re an astronaut being paid according to the time you spend traveling in space. You take a long voyage traveling at a speed near that of light. Upon your return to Earth, you’re asked how you’d like to be paid: according to the time elapsed on a clock on Earth or according to your ship’s clock. To maximize your paycheck, which should you choose?
a) the Earth clock
b) the ship’s clock
c) either clock because it doesn’t make a difference
3.Suppose you take a trip to Mars, which is 80 million km from the Earth. You head directly toward Mars onboard your spaceship, traveling at 0.80c. Unbeknownst to you, your mortal enemy placed a bomb on your ship that has a 4-minute timer that was initiated upon your departure. Will you live long enough to reach Mars? Answer the problem first without relativity and then using relativity from both your point of view and that of your Earth-bound enemy.
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4.An enemy spaceship is moving toward your star fighter with a speed, as measured in your frame, of 0.400c. The enemy ship fires a missile toward you at a speed of 0.700c relative to the enemy ship
(a) What is the speed of the missile relative to you? Express your answer in terms of the speed of light
(b) If you measure that the enemy ship is 8.00 x 106km away from you when the missile is fired, how much time, measured in your frame, will it take the missile to reach you?
5.Caught by surprise near a supernova, you race away from the explosion in your spaceship, hoping to outrun the high-speed material ejected toward you. Your Lorentz factor y relative to the inertial reference frame of the local stars is 22.4.
(a) To reach a safe distance, you figure you need to cover 9.00 x 1016 m as measured in the reference frame of the local stars. How long will the flight take, as measured in that frame?
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