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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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You fly \(32.0{\rm{ km}}\) in a straight line in still air in the direction \(35.0^\circ \) south of west.
(a) Find the distances you would have to fly straight south and then straight west to arrive at the same point. (This determination is equivalent to finding the components of the displacement along the south and west directions.)
(b) Find the distances you would have to fly first in a direction \(45.0^\circ \) south of west and then in a direction \(45.0^\circ \) west of north. These are the components of the displacement along a different set of axes鈥攐ne rotated \(45.0^\circ \).
Construct Your Own Problem Consider an airplane headed for a runway in a cross wind. Construct a problem in which you calculate the angle the airplane must fly relative to the air mass in order to have a velocity parallel to the runway. Among the things to consider are the direction of the runway, the wind speed and direction (its velocity) and the speed of the plane relative to the air mass. Also calculate the speed of the airplane relative to the ground. Discuss any last minute maneuvers the pilot might have to perform in order for the plane to land with its wheels pointing straight down the runway.
Verify the ranges for the projectiles in Figure 3.41 (a) for and the given initial velocities.
The free throw line in basketball is from the basket, which is above the floor. A player standing on the free throw line throws the ball with an initial speed of releasing it at a height of above the floor. At what angle above the horizontal must the ball be thrown to exactly hit the basket? Note that most players will use a large initial angle rather than a flat shot because it allows for a larger margin of error. Explicitly show how you follow the steps involved in solving projectile motion problems.
An archer shoots an arrow at a distant target; the bull鈥檚-eye of the target is at same height as the release height of the arrow.
(a) At what angle must the arrow be released to hit the bull鈥檚-eye if its initial speed is ? In this part of the problem, explicitly show how you follow the steps involved in solving projectile motion problems.
(b) There is a large tree halfway between the archer and the target with an overhanging horizontal branch above the release height of the arrow. Will the arrow go over or under the branch?
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