CHAPTER
3
KINEMATICS IN
TWO DIMENSIONS
ANSWERS TO FOCUS ON CONCEPTS QUESTIONS
1.
(a)
The horizontal component
v
x
of the projectile’s velocity remains constant throughout the
motion, since the acceleration
a
x
in the horizontal direction is zero (
a
x
= 0 m/s
2
). The
vertical component
v
y
, however, changes as the projectile moves. This component is greatest
at point 1, decreases to zero at point 2 at the top of the trajectory, and then increases to a
magnitude less than that at point 1 as the projectile approaches point 3.
3.
(c)
The acceleration due to gravity is the same for both balls, despite the fact that they have
different velocities.
4.
(d)
The acceleration of a projectile is the same at all points on the trajectory. It points
downward, toward the earth, and has a magnitude of 9.80 m/s
2
.
6.
(c)
The time for a projectile to reach the ground depends only on the
y
component (or
vertical component) of its variables, i.e.,
y
,
v
0
y
, and
a
y
. These variables are the same for both
balls. The fact that Ball 1 is moving horizontally at the top of its trajectory does not play a
role in the time it takes for it to reach the ground.
14. (c)
The velocity
v
PC
of the passenger relative to the car is given by
v
PC
=
v
PB
+
v
BC
,
according to the subscripting method discussed in Section 3.4. However, the last term on the
right of this equation is given by
v
BC
=
v
BG
+
v
GC
.
So,
v
PC
=
v
PB
+
v
BG
+
v
GC
=
+2 m/s + 16 m/s + (
−
12 m/s) = +6 m/s.
16.
The magnitude
v
AB
of the velocity of car A relative to car B is
v
AB
= 34.2 m/s. The angle
that the velocity
v
AB
makes with respect to due east is
θ
= 37.9
°
south of east.