Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 21, Problem 5CC
To determine
At what speed the light is coming from one spaceship as observed by observer in another spaceship and as observed by an observer on a stationary planet at the midway, given that the two spaceships are traveling at 90% of the
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Draw a third quadrant vector C. (remember that boldface characters represent vector
quantities). Show the standard angle 0 for this vector (= angle that C makes with the positive x-
axis). Also show the angle that C makes with the negative y-axis: call the latter angle 8. Finally,
show the smallest angles that C makes with the positive x-axis and the positive y-axis: call these
angles p1 and p2, repectively.
a) Prove the following formulas for the components of C involving the standard angle (hint:
start with the formulas for the components based on the angle & and then use (look up if
necessary) co-function identities linking cosine and sine of 8 to sine and cosine of 0 since 8 =
3π/2-8 (this will switch cosine and sine around and eliminate - signs as well))
-
C=Ccose
C₁=Csine
b) Prove the following formulas for the components of C:
C=Ccosp1
C=Ccosp2
Notation matters when working with vectors! In particular, it is important to
distinguish between the vector itself (A) and its magnitude (A).
Illustrate in four separate sketches that each of the following statements is
possible:
a) both R = A + B and R=A+B are correct
b) R = A + B is correct, but R=A+B is incorrect
c) R = A + B is incorrect, but R=A+B is correct
d) both R = A + B and R=A+B are incorrect
You know from your math courses that an infinitesimal segment of a
circular arc can be considered as a straight line segment. Imagine that you
cover a full circle in, say, the clockwise direction, with infinitesimal
displacement vectors dr. Then evaluate fdr and fdr (the circle symbol on
the integral just reminds us that we have to go around the full circle).
Chapter 21 Solutions
Universe
Ch. 21 - Prob. 1CCCh. 21 - Prob. 2CCCh. 21 - Prob. 3CCCh. 21 - Prob. 4CCCh. 21 - Prob. 5CCCh. 21 - Prob. 6CCCh. 21 - Prob. 7CCCh. 21 - Prob. 8CCCh. 21 - Prob. 9CCCh. 21 - Prob. 10CC
Ch. 21 - Prob. 11CCCh. 21 - Prob. 12CCCh. 21 - Prob. 13CCCh. 21 - Prob. 14CCCh. 21 - Prob. 15CCCh. 21 - Prob. 16CCCh. 21 - Prob. 17CCCh. 21 - Prob. 18CCCh. 21 - Prob. 19CCCh. 21 - Prob. 20CCCh. 21 - Prob. 21CCCh. 21 - Prob. 1QCh. 21 - Prob. 2QCh. 21 - Prob. 3QCh. 21 - Prob. 4QCh. 21 - Prob. 5QCh. 21 - Prob. 6QCh. 21 - Prob. 7QCh. 21 - Prob. 8QCh. 21 - Prob. 9QCh. 21 - Prob. 10QCh. 21 - Prob. 11QCh. 21 - Prob. 12QCh. 21 - Prob. 13QCh. 21 - Prob. 14QCh. 21 - Prob. 15QCh. 21 - Prob. 16QCh. 21 - Prob. 17QCh. 21 - Prob. 18QCh. 21 - Prob. 19QCh. 21 - Prob. 20QCh. 21 - Prob. 21QCh. 21 - Prob. 22QCh. 21 - Prob. 23QCh. 21 - Prob. 24QCh. 21 - Prob. 25QCh. 21 - Prob. 26QCh. 21 - Prob. 27QCh. 21 - Prob. 28QCh. 21 - Prob. 29QCh. 21 - Prob. 30QCh. 21 - Prob. 31QCh. 21 - Prob. 32QCh. 21 - Prob. 33QCh. 21 - Prob. 34QCh. 21 - Prob. 35QCh. 21 - Prob. 36QCh. 21 - Prob. 37QCh. 21 - Prob. 38QCh. 21 - Prob. 39QCh. 21 - Prob. 40QCh. 21 - Prob. 41QCh. 21 - Prob. 42QCh. 21 - Prob. 43QCh. 21 - Prob. 44QCh. 21 - Prob. 45QCh. 21 - Prob. 46QCh. 21 - Prob. 47QCh. 21 - Prob. 48QCh. 21 - Prob. 49QCh. 21 - Prob. 50QCh. 21 - Prob. 51QCh. 21 - Prob. 52QCh. 21 - Prob. 53QCh. 21 - Prob. 54QCh. 21 - Prob. 55QCh. 21 - Prob. 56QCh. 21 - Prob. 57QCh. 21 - Prob. 58QCh. 21 - Prob. 59QCh. 21 - Prob. 60QCh. 21 - Prob. 61QCh. 21 - Prob. 62QCh. 21 - Prob. 63QCh. 21 - Prob. 64QCh. 21 - Prob. 65QCh. 21 - Prob. 66QCh. 21 - Prob. 67QCh. 21 - Prob. 68QCh. 21 - Prob. 69QCh. 21 - Prob. 70QCh. 21 - Prob. 71QCh. 21 - Prob. 72QCh. 21 - Prob. 73QCh. 21 - Prob. 74QCh. 21 - Prob. 75QCh. 21 - Prob. 85QCh. 21 - Prob. 86Q
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