An inertial frame of reference is one in which Newton's laws hold. Any frame of reference that moves at a constant speed relative to an inertial frame of reference is also an inertial frame. The proper length of an object is defined to be the length of the object as measured in the object's rest frame. If the length of the object is measured in any other inertial frame, moving with speed u relative to the object's rest frame (in a direction parallel to Lo), the resulting length is given by the length contraction equation L = Lo√√1-u²/c² where c is the speed of light. Similarly, if two events occur at the same spatial point in a particular reference frame, and an observer at rest in this frame measures the time interval between these two events, the time interval so measured is defined to be the proper time to. When the time interval is measured in any other inertial frame, again moving with speed u relative to the first frame, the resulting time interval t is given by the time dilation equation, t = to/√1-u²/c² Two spaceships, named A and B, are flying toward each other with relative speed 0.8 c. The captain of ship A fires a missile that is 2 m long at ship B. The captain of ship B measures the length of the missile as 1.57 m. What is the speed of the missile relative to ship B? Express answer as a fraction of c.
An inertial frame of reference is one in which Newton's laws hold. Any frame of reference that moves at a constant speed relative to an inertial frame of reference is also an inertial frame. The proper length of an object is defined to be the length of the object as measured in the object's rest frame. If the length of the object is measured in any other inertial frame, moving with speed u relative to the object's rest frame (in a direction parallel to Lo), the resulting length is given by the length contraction equation L = Lo√√1-u²/c² where c is the speed of light. Similarly, if two events occur at the same spatial point in a particular reference frame, and an observer at rest in this frame measures the time interval between these two events, the time interval so measured is defined to be the proper time to. When the time interval is measured in any other inertial frame, again moving with speed u relative to the first frame, the resulting time interval t is given by the time dilation equation, t = to/√1-u²/c² Two spaceships, named A and B, are flying toward each other with relative speed 0.8 c. The captain of ship A fires a missile that is 2 m long at ship B. The captain of ship B measures the length of the missile as 1.57 m. What is the speed of the missile relative to ship B? Express answer as a fraction of c.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:An inertial frame of reference is one in which Newton's laws hold. Any frame of reference that
moves at a constant speed relative to an inertial frame of reference is also an inertial frame. The
proper length of an object is defined to be the length of the object as measured in the object's
rest frame. If the length of the object is measured in any other inertial frame, moving with speed
u relative to the object's rest frame (in a direction parallel to Lo), the resulting length is given by
the length contraction equation
L = Lo√√1-u²/c²
where c is the speed of light. Similarly, if two events occur at the same spatial point in a
particular reference frame, and an observer at rest in this frame measures the time interval
between these two events, the time interval so measured is defined to be the proper time to.
When the time interval is measured in any other inertial frame, again moving with speed u
relative to the first frame, the resulting time interval t is given by the time dilation equation,
t = to/√1-u²/c²
Two spaceships, named A and B, are flying toward each other with relative speed 0.8 c. The
captain of ship A fires a missile that is 2 m long at ship B. The captain of ship B measures the
length of the missile as 1.57 m. What is the speed of the missile relative to ship B? Express
answer as a fraction of c.
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