6) A rocket is moving at 0.7c. mz mssiles a) According to an observer on the rocket it launches a missile in the same direction it is moving with a speed of 0.4c. An observer on the ground measures the speed of the missile. What velocity does she measure? Please answer in terms of c. b) If the same rocket launched the same missile in a direction opposite to the motion of the rocket, what would the velocity seen from the observer on the ground be? What is its direction as seen from the ground? Hint: The addition of velocities requires a special formula which was in the lectures. To figure out how to use it start with the non-relativisitc version: V 12 = V13 + V32 then modify it with the correct denominator to make it relativistic: V12 = (V13+ V32)/(1+(V13 V32/c²)). Pay careful attention to the signs of the velocities. If you end up with a speed larger than the speed of light you have made a mistake.

6) A rocket is moving at 0.7c. mz mssiles a) According to an observer on the rocket it launches a missile in the same direction it is moving with a speed of 0.4c. An observer on the ground measures the speed of the missile. What velocity does she measure? Please answer in terms of c. b) If the same rocket launched the same missile in a direction opposite to the motion of the rocket, what would the velocity seen from the observer on the ground be? What is its direction as seen from the ground? Hint: The addition of velocities requires a special formula which was in the lectures. To figure out how to use it start with the non-relativisitc version: V 12 = V13 + V32 then modify it with the correct denominator to make it relativistic: V12 = (V13+ V32)/(1+(V13 V32/c²)). Pay careful attention to the signs of the velocities. If you end up with a speed larger than the speed of light you have made a mistake.

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter38: Relativity

Section: Chapter Questions

Problem 6P: An astronaut is traveling in a space vehicle moving at 0.500c relative to the Earth. The astronaut...

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Suppose our Sun is about to explode. In an effort to escape, we depart in a spacecraft at v = 0.800c and head toward the star Tau Ceti, 12.0 ly away. When we reach the midpoint of our journey from the Earth, we see our Sun explode, and, unfortunately, at the same instant, we see Tau Ceti explode as well. (a) In the spacecrafts frame of reference, should we conclude that the two explosions occurred simultaneously? If not, which occurred first? (b) What If? In a frame of reference in which the Sun and Tau Ceti are at rest, did they explode simultaneously? If not, which exploded first?
Two identical spaceships with proper lengths of 175 m are launched from Earth. Spaceship A is launched in one direction at 0.500c and spaceship B is launched in the opposite direction at 0.750c. (a) What is the speed of spaceship B relative to spaceship A? (b) What is the length of spaceship A as measured by astronauts on spaceship B?
If two spaceships are heading directly towards each other at 0.800c, at what speed must a canister be shot from the first ship to approach the other at 0.999c as seen by the second ship?
Suppose a spaceship heading straight towards the Earth at 0.750c can shoot a canister at 0.500c relative to the ship. (a) What is the velocity of the canister relative to the Earth, if it is shot directly at the Earth? (b) If it is shot directly away from the Earth?
An alien spaceship traveling at 0.600c toward the Earth launches a landing craft. The landing craft travels in the same direction with a speed of 0.800r relative to the mother ship. As measured on the Earth, the spaceship is 0.200 ly from the Earth when the landing craft is launched, (a) What speed do the Earth-based observers measure for the approaching landing craft? What is the distance to the Earth at the moment of the landing craft's launch as measured by the aliens? What travel time is required for the landing craft to reach the Earth as measured by the aliens on the mother ship? (d) If' the landing craft has a mass of 4.00 10s kg. what is its kinetic energy as measured in the Earth reference frame?
An alarm clock is set to sound in 10.0 h. At t = 0, the clock is placed in a spaceship moving with a speed of 0.75c (relative to Earth). What distance, as determined by an Earth observer, does the spaceship travel before the alarm clock sounds?
Two planets are on a collision course, heading directly toward each other at 0.250c. A spaceship sent from one planet approaches the second at 0.750c as seen by the second planet. What is the velocity of the ship relative to the first planet?
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 spacecraft built in the shape of a sphere moves past an observer on the Earth with a speed of 0.500c. What shape does the observer measure for the spacecraft as it goes by? (a) a sphere (b) a cigar shape, elongated along the direction of motion (c) a round pillow shape, flattened along the direction of motion (d) a conical shape, pointing in the direction of motion
A spaceship, 200 m long as seen on board, moves by the Earth at 0.970c. What is its length as measured by an Earth-bound observer?
(a) All but the closest galaxies are receding from our own Milky Way Galaxy. If a galaxy 12.0109ly ly away is receding from us at 0. 0.900c, at what velocity relative to us must we send an exploratory probe to approach the other galaxy at 0.990c, as measured from that galaxy? (b) How long will it take the probe to reach the other galaxy as measured from the Earth? You may assume that the velocity of the other galaxy remains constant. (c) How long will it then take for a radio signal to be beamed back? (All of this is possible in principle, but not practical.)
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?