e) 644 nm 20. The distance between two far away stars is 6.80 light years. A spacecraft travels froll star to the other at a constant velocity. According to a passenger in the spacecraft, the trip lasts 8.70 years. Find the speed of the spacecraft. a) 0.616c b) 0.533c c) 0.884c d) 0.782c e) 0.435c 100 Mey of kinetic energy, what is its speed?

e) 644 nm 20. The distance between two far away stars is 6.80 light years. A spacecraft travels froll star to the other at a constant velocity. According to a passenger in the spacecraft, the trip lasts 8.70 years. Find the speed of the spacecraft. a) 0.616c b) 0.533c c) 0.884c d) 0.782c e) 0.435c 100 Mey of kinetic energy, what is its speed?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter26: Relativity

Section: Chapter Questions

Problem 14CQ: Imagine an astronaut on a trip to Sirius, which lies 8 light-years from Earth. Upon arrival at...

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(a) Suppose the speed of light were only 3000 m/s. A jet fighter moving toward a target on the ground at 800 m/s shoots bullets, each having a muzzle velocity of 1000 m/s. What are the bullets' velocity relative to the target? (b) If the speed of light was this small, would you observe relativistic effects in everyday life? Discuss.
An alien spaceship traveling 0.600c toward Earth launches a landing craft with an advance guard of purchasing agents. The lander travels in the same direction with a velocity 0.800c relative to the spaceship. As observed on Earth, the spaceship is 0.200 light-years from Earth when the lander is launched. (a) With what velocity is the lander observed to be approaching by observers on Earth? (b) What is the distance to Earth at the time of landcr launch, as observed by the aliens on the mother ship? (c) How long does it take the lander to reach Earth as observed by the aliens on the mother ship? (d) If the lander has a mass of 4.00 105 kg, what is its kinetic energy as observed in Earths reference frame?
A spaceship moves past Earth with a speed of 0.900c. As it is passing, a person on Earth measures the spaceship's length to be 75.0 m. (a) Determine the spaceships proper length. (b) Determine the time required for the spaceship to pass a point on Earth as measured by a person on Earth and (c) by an astronaut onboard the spaceship.
A spaceship moves past Earth with a speed of 0.900c. As it is passing, a person on Earth measures the spaceship's length to be 75.0 m. (a) Determine the spaceships proper length. (b) Determine the time required for the spaceship to pass a point on Earth as measured by a person on Earth and (c) by an astronaut onboard the spaceship.
A physics professor on the Earth gives an exam to her students, who are in a spacecraft traveling at speed v relative to the Earth. The moment the craft passes the professor, she signals the start of the exam. She wishes her students to have a time interval T0 (spacecraft time) to complete the exam. Show that she should wait a time interval (Earth time) of T=T01/c1+/c before sending a light signal telling them to stop. (Suggestion: Remember that it takes some time for the second light signal to travel from the professor to the students.)
Imagine an astronaut on a trip to Sirius, which lies 8 light-years from Earth. Upon arrival at Sirius, the astronaut finds that the trip lasted 6 years. If the trip was made at a constant speed of 0.8c, how can the 8-light-year distance be reconciled with the 6-year duration?
A pulsar is a stellar object that emits light in short bursts. Suppose a pulsar with a speed of 0.950c approaches Earth, and a rocket with a speed of 0.995c heads toward the pulsar. (Both speeds are measured in Earth's frame of reference.) If the pulsar emits 10.0 pulses per second in its own frame of reference, at what rate are the pulses emitted in the rockets frame of reference?
An astronaut wishes to visit the Andromeda galaxy, making a one-way trip that will take 30.0 years in the space-ships frame of reference. Assume the galaxy is 2.00 million light-years away and his speed is constant. (a) How fast must he travel relative to Earth? (b) What will be the kinetic energy of his spacecraft, which has mass of 1.00 106 kg? (c) What is the cost of this energy if it is purchased at a typical consumer price for electric energy, 13.0 cents per kWh? The following approximation will prove useful: 11+x1x2forx1
An interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 70.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 15.0 years as measured in a rest frame. (a) How long do the batteries on the space probe last as measured by mission control on Earth? (b) How far is the probe from Earth when its batteries fail as measured by mission control? (c) How far is the probe from Earth as measured by its built-in trip odometer when its batteries fail? (d) For what total time after launch are data received from the probe by mission control? Note dial radio waves travel at the speed of light and fill the space between the probe and Earth at the time the battery fails.
An astronaut is traveling in a space vehicle that has a speed of 0.500c relative to Earth. The astronaut measures his pulse rate at 75.0 beats per minute. Signals generated by the astronauts pulse are radioed to Earth when the vehicle is moving perpendicular to a line that connects the vehicle with an Earth observer. (a) What pulse rate does the Earth observer measure? (b) What would be the pulse rate if the speed of the space vehicle were increased to 0.990c?
Unreasonable Results A spaceship is heading directly toward Earth at a velocity of 0.800c. The astronaut on board claims that he can send a canister toward the Earth at 1.20c relative to Earth. (a) Calculate the velocity the canister must have relative to the spaceship. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
If astronauts could travel at v = 0.950c, we on Earth would say it takes (4.20/0.950) = 4.42 years to reach Alpha Centauri, 4.20 light-years away. The astronauts disagree. (a) How much time passes on the astronauts clocks? (b) What is the distance to Alpha Centauri as measured by the astronauts?