A particle moves along the x' axis of frame S' with velocity 0.33c. Frame S' moves with velocity 0.65c with respect to frame S. What is the speed of the particle with respect to frame S? Number i Units eTexthook and Medie

A particle moves along the x' axis of frame S' with velocity 0.33c. Frame S' moves with velocity 0.65c with respect to frame S. What is the speed of the particle with respect to frame S? Number i Units eTexthook and Medie

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter39: Relativity

Section: Chapter Questions

Problem 39PQ: As measured in a laboratory reference frame, a linear accelerator ejects a proton with a speed of...

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Owen and Dina are at rest in frame S, which is moving with a speed of 0.600c with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action (Fig. P26.45). Owen throws the ball to Dina with a speed of 0.800c (according to Owen) and their separation (measured in S) is equal to 1.80 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, and (d) how fast is the ball moving? Figure. P26.45
Owen and Dina are at rest in frame S, which is moving with a speed of 0.600c with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action (Fig. P26.45). Owen throws the ball to Dina with a speed of 0.800c (according to Owen) and their separation (measured in S) is equal to 1.80 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, and (d) how fast is the ball moving? Figure. P26.45
In a frame S, two events are observed: event 1: a pion is created at rest at the origin and event 2: the pion disintegrates after time Another observer in a frame S' is moving in the positive direction along the positive x-axis with a constant speed v and observes the same two events in his frame. The origins of the two frames coincide at (a) Find the positions and timings of these two events in the frame S' (a) according to the Galilean transformation, and (b) according to the Lorentz transformation.
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 observer in reference frame S sees two events as simultaneous. Event A occurs at the point (50.0 m, 0, 0) at the instant 9:00:00 Universal time, 15 January 2001. Event B occurs at the point (150 m, 0, 0) at the same moment. A second observer, moving past with a velocity of , also observes the two events. In her reference frame S′, which event occurred first and what time elapsed between the events?
(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.
(a) How long would the muon in Example 28.1 have lived as observed on the Earth if its velocity was 0.0500c ? (b) How far would it have traveled as observed on the Earth? (c) What distance is this in the muon's frame?
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?
(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.)
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.
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?