Problem 3.
32
To get to a concert in time, a harpsichordist has to drive 122 mi in 2.00 h. (a) If he drove at an average
speed of 55.0 mi/h in a due west direction for the first 1.20 h, what must be his average speed if he is
heading 30.0° south of west
for the remaining 48.0 min? (b) What is his average velocity for the entire trip?
What do we want to know in a? the speed
a)
speed
we don’t care about the direction, would it be
west,
north
west east
to solve a
!!!!
What do we know, the total length of th
e trip, we know can calculate the length already gone
through having the velocity and the time and from there the length still to go though and the
Time left, so the average speed of the remaining part
And the time left so we can can calculate the average
speed of the remaining part
If he drove at
an average
speed
of
55.0 m/h for 1.2h, he drove 55.0m/hx1.2
0
h= 66.0 miles out of
The
122 miles, the distance left to dri
ve is 122

66.0 = 56
.0
miles and the time left is
2
.00
h
1.2
0
h=0.80 h
so the average
speed
in that remaining
part o
f the trip should be
56/0.80=70
m/h
What do we want to know
the average velocity ?
b)
velocity
, we do care about directions !!!!!
The average
velocity
for the entire trip,
is the tota
l displacement divided by the 2 hours,
Namely
r/2hours
r=v(
x
2
+
y
2
)
x = 55.0m/h*1.2
0 h + 56
(cos30)=114.5 mi
y = 56sin(30) = 28
mi
v=
r/
t=v(114.6
2
+28
2
) /
2.00
=
59mi/h
= tan
1
(28/114.5) = 14 deg South of West
30deg
S
W
r
N
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Problem 3.23.
Vector
has magnitude 7.1 and direction 14° below the +
x
axis. Vector
has
x

component
C
x
=
–
1.8
and
y component
C
y
=
–
6.7. Compute (a) the
x

and
y
co
mponents of
; (b) the magnitude and direction of
; (c) the magnitude and direction of
+
; (d) the magnitude and direction of
–
; (e) the
x

and
y

components of
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 Spring '09
 HUANG
 Acceleration, Velocity, vyi

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