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Chapter 3: Q.10CQ (page 119)
Give an example of a nonzero vector that has a component of zero.
If a vector is acting along a particular axis, either x or y axis, then the component of the vector other than its direction will be zero.
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Suppose a pilot fliesin a direction north of east and then flies in a direction role="math" localid="1668679997174" north of east as shown in Figure 3.63. Find her total distance from the starting point and the direction of the straight-line path to the final position. Discuss qualitatively how this flight would be altered by a wind from the north and how the effect of the wind would depend on both wind speed and the speed of the plane relative to the air mass.
Suppose you first walk 12.0 m in a direction 20潞 west of north and then 20.0 m in a direction 40.0潞 south of west. How far are you from your starting point and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B , as in Figure 3.56, then this problem finds their sum R = A + B.)
Find the following for path C in Figure
(a) the total distance traveled and
(b) the magnitude and direction of the displacement from start to finish.
In this part of the problem, explicitly show how you follow the steps of the analytical method of vector addition.
Figure: The various lines represent paths taken by different people walking in a city. All blocks are \(120{\rm{ m}}\) on a side.
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.
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?
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