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Chapter 3: Q1CQ (page 118)
Which of the following is a vector: a person鈥檚 height, the altitude on Mt. Everest, the age of the Earth, the boiling point of water, the cost of this book, the Earth鈥檚 population, the acceleration of gravity?
Acceleration due to gravity is only a vector quantity.
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Find the magnitudes of velocities\({v_A}\)and\({v_B}\)in Figure 3.57.
The two velocities\({{\rm{v}}_{\rm{A}}}\)and\({{\rm{v}}_{\rm{B}}}\)add to give a total \({{\rm{v}}_{{\rm{tot}}}}\).
Prove that the trajectory of a projectile is parabolic, having the form . To obtain this expression, solve the equation for and substitute it into the expression for (These equations describe the xand y positions of a projectile that starts at the origin.) You should obtain an equation of the form where a and bare constants.
A projectile is launched at ground level with an initial speed ofat an angle ofabove the horizontal. It strikes a target above the groundseconds later. What are the x and y distances from where the projectile was launched to where it lands?
The great astronomer Edwin Hubble discovered that all distant galaxies are receding from our Milky Way Galaxy with velocities proportional to their distances. It appears to an observer on the Earth that we are at the center of an expanding universe. The figure illustrates this for five galaxies lying along a straight line, with the Milky Way Galaxy at the center. Using the data from the figure, calculate the velocities:
(a) relative to galaxy 2
(b) relative to galaxy 5.
The results mean that observers on all galaxies will see themselves at the center of the expanding universe, and they would likely be aware of relative velocities, concluding that it is not possible to locate the center of expansion with the given information.
Suppose you add two vectors A and B. What relative direction between them produces the resultant with the greatest magnitude? What is the maximum magnitude? What relative direction between them produces the resultant with the smallest magnitude? What is the minimum magnitude?
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