Ch 3: Solutions, Part b
Questions
6. If the two vectors are in the same direction, the magnitude o f their sum wi ll be a maximum, and wi ll
be 7.5 km. If the two vectors are in the opposite direction, the magnitude of their sum will be a
minimum, and will be 0.5 km. If the two vec tors are oriented in any other configuration, the
magnitude of their su m will be betwe en 0.5 km and 7.5 km.
8. (a) The magnitude of a v ector can equ al the length of one of its components if the other
components of the vector are all 0; i.e., if the vector lies along one of the coordinate axe s.
(b) The magnitude of a vector can never be less th an one of its components, because each
component contributes a positive amount to the over all magnitude, through the Pythagorean
relationship. The square root of a sum of squares is never less than the absolute value of any
individual term.
9. A particle with constant speed can be accelerating, if its direction is changing. Driving on a curved
roadway at constant speed would be an example. However, a particle with constant velocity cannot
be accelerating – its acceleration mus t be zero. It has bo th constant speed and constant direction.
11. Assume that the bul let was fired from behind and below the airplane. As the bullet rose in the air, its
vertical speed would be slowed by both gravity and air resistance, and its horizontal speed would be
slowed by air resistance. If the altitude of the a irplane was slightly below the maximum height of the
bullet, then at the altitude of the airplane, the bullet would be moving qu ite slowly in th e vertical
direction. If th e bullet’s horizontal speed had also s lowed enough to approximately match the speed
of the a irplane, then the bullet’s velocity relative to the airplane would be small. With the bullet
moving slowly, it could safely be caught by hand.
Problems:
17. Choose downward to be the positive y direction. The origin will be at the point wh ere the tiger leaps
from the rock. In the horizontal direction,
sm 5.3
0=
x
v
and
.0=
x
a
In the vertical direction,
,0 ,sm 80.9 ,0 0
2
0=== yav yy
and the f inal location
m. 5.6=y
The time for the tiger to rea ch the
