Matter and Interactions
4th Edition
ISBN: 9781118875865
Author: Ruth W. Chabay, Bruce A. Sherwood
Publisher: WILEY
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Chapter 1, Problem 35P
To determine
Velocity vector of the asteroid.
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Draw a right-handed 3D Cartesian coordinate system (= x, y and z axes). Show a vector A with
tail in the origin and sticking out in the positive x, y and z directions. Show the angles between A
and the positive x, y and z axes, and call these angles α₁, α₂ and α3
Prove that Ax Acos α₁
Ay
= Acos α₂
A₂- Acos α3
solve for Vo
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
Chapter 1 Solutions
Matter and Interactions
Ch. 1.2 - (a) Which of the following do you see moving with...Ch. 1.3 - (a) Apply Newton’s first law to each of the...Ch. 1.4 - You stand at location m. Your friend stands at...Ch. 1.4 - If m/s, what is ?
Ch. 1.4 - (a) Consider the vectors and represented by...Ch. 1.4 - Which of the following statements about the three...Ch. 1.4 - At 10:00 am you are al location 〈−3,2,5〉 m. By...Ch. 1.4 - Prob. 9CPCh. 1.5 - A snail moved 80 cm (80 centimeters) in 5 min....Ch. 1.6 - At a time 0.2 s after it has been hit by a tennis...
Ch. 1.7 - A proton traveling with a velocity of 〈3 × 105, 2...Ch. 1.7 -
Figure 1.41 A comet goes around a star.
A comet...Ch. 1.7 - (a) Powerful sports cars can go from zero to 25...Ch. 1.8 - The planet Mars has a mass of 6.4 × 1023 kg, and...Ch. 1.9 - At time t1 = 12 s, a car with mass 1300 kg is...Ch. 1.10 - What is the result of multiplying the vector by...Ch. 1.12 - A spaceship at rest with respect to the cosmic...Ch. 1 - Prob. 1QCh. 1 - In the periodic table on the inside front cover of...Ch. 1 - Which of the following observers might observe...Ch. 1 - Prob. 4QCh. 1 - Which of the following statements about the...Ch. 1 - Answer the following questions about the factor γ...Ch. 1 - Prob. 7QCh. 1 - Moving objects left the traces labeled A–F in...Ch. 1 - A car moves along a straight road. It moves at a...Ch. 1 - A spaceship far from all other objects uses its...Ch. 1 - Which of the following are vectors? (a) /2 (b)...Ch. 1 - Figure 1.55 shows several arrows representing...Ch. 1 - What is the magnitude of the vector , where = 〈8 ×...Ch. 1 - In Figure 1.56 three vectors are represented by...Ch. 1 - The following questions refer to the vectors...Ch. 1 - On a piece of graph paper, draw arrows...Ch. 1 - What is the result of multiplying the vector by...Ch. 1 - What is the unit vector in the direction of 〈2, 2,...Ch. 1 - (a) On a piece of graph paper, draw the vector =...Ch. 1 - Write the vector = 〈400, 200, −100〉 m/s2 as the...Ch. 1 - Prob. 22PCh. 1 - A proton is located at 〈3 × 10−10, −3 × 10−10, 8 ×...Ch. 1 - In Figure 1.59, the vector 1 points to the...Ch. 1 - (a) What is the vector whose tail is at 〈9.5, 7,...Ch. 1 - A man is standing on the roof of a building with...Ch. 1 - A star is located at 〈6 × 1010, 8 × 1010, 6 ×...Ch. 1 - A planet is located at ⟨−1 × 1010, 8 × 1010, −3 ×...Ch. 1 - A proton is located at 〈xp, yp, zp〉. An electron...Ch. 1 - A cube is 3 cm on a side, with one corner at the...Ch. 1 - Prob. 31PCh. 1 - Prob. 32PCh. 1 - Prob. 33PCh. 1 - Prob. 34PCh. 1 - Prob. 35PCh. 1 - A spacecraft traveling at a velocity of 〈−20, −90,...Ch. 1 - Here are the positions at three different times...Ch. 1 - Prob. 38PCh. 1 - Prob. 39PCh. 1 - Prob. 40PCh. 1 - At a certain instant a ball passes location 〈7,...Ch. 1 - You throw a ball. Assume that the origin is on the...Ch. 1 - Figure 1.60 shows the trajectory of a ball...Ch. 1 - Prob. 44PCh. 1 - Prob. 45PCh. 1 - Prob. 46PCh. 1 - Prob. 47PCh. 1 - Prob. 48PCh. 1 - Prob. 49PCh. 1 - Prob. 50PCh. 1 - A tennis ball of mass m traveling with velocity...Ch. 1 - Prob. 52PCh. 1 - Prob. 53PCh. 1 - Prob. 54PCh. 1 - Prob. 55PCh. 1 - Figure 1.61 shows a portion of the trajectory of a...Ch. 1 - Prob. 57PCh. 1 - Prob. 58PCh. 1 - Prob. 59PCh. 1 - Prob. 60PCh. 1 - A proton in an accelerator attains a speed of...Ch. 1 - Prob. 62PCh. 1 - Prob. 63PCh. 1 - Prob. 64PCh. 1 - Prob. 65PCh. 1 - An electron travels at speed || = 0.996c, where c...Ch. 1 - Prob. 67P
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