SOLUTION TO
HOMEWORK PROBLEMS Chapter 3: VECTORS
1. A fly lands on one wall of a room. The lower-left corner of the wall is selected as the origin
of a two-dimensional Cartesian coordinate system. If the fly is located at the point having
coordinates (3.00, 1.50) m, what is its location in polar coordinates?
θ = tan-1 (y/x) > θ = tan-1(1.5/3.0) > θ = 26.6
x = r Cos θ > r = 3.00 / cos 26.6 > r = 3.35
2. A surveyor measures the distance across a straight river by the following method. Starting
directly across from a tree on the opposite bank, she walks d = 138 m along the riverbank to
establish a baseline. Then she sights across to the tree. The angle from her baseline to the tree is
= 35.0°. How wide is the river?
Tan 35 = y / d > y = 0.7 * 138 = 96.6 m
3. A force
1
F
of magnitude 6.00 units acts on an object at the origin in a direction
= 30.0°
above the positive x axis. A second force
2
F
of magnitude 5.00 units acts on the object in the
direction of the positive x axis. Find magnitude and direction of the resultant force
12
FF
6Cos30i + 5i + 6sin30j = (5.2+5)i + 3j > mag = √(10.22 + 32) = 10.6 N
θ = tan-1 (3/10.2) = 16.4
4. A person walks 25.0° north of east for 3.10 km. How far would she have to walk due south
and due west to return to the starting point?
W = 3.10 Cos 25 = 2.81 km
S = 3.10 Sin 25 = 1.31 km
5. A map suggests that Atlanta is 730 miles in a direction of 5.00° north of east from Dallas.
The same map shows that Chicago is 560 miles in a direction of 21.0° west of north from Atlanta.
(Figure P3.22 shows the locations of these three cities.) Modeling the Earth as flat, use this
information to find the displacement from Dallas to Chicago.
DC east DA east AC east
DC nort h DA north AC nort h
+ 730cos 5.00 560sin 21.0 527 miles
+ 730sin 5.00 +560cos 21.0 586 miles
d d d
d d d
By the Pythagorean theorem,
22
DC east DC north
( ) ( ) 788 mid d d
.
Then
DC north
DC east
tan 1.11
d
d
and
48.0
.
