Conceptual Physics

3.3 What is the polar notation for a vector that points from the origin to the point (0, 3.00)?

( , °)

Section 4 - Vector components and rectangular notation

4.1 (a) A hotdog vendor named Sam is walking from the southwest corner of Central park to the Empire State Building. He starts

at the intersection of 59th Street and Eighth Avenue, walks 3 blocks east to 59th Street and Fifth Avenue, and then 25 blocks

south to the Empire State Building at the Corner of 34th Street and Fifth Avenue. Write his displacement vector in rectangular

notation with units of "blocks." Orient the axes so positive y is to the north, and positive x is to the east. (b) A stockbroker

named Andrea makes the same trip in a cab that gets lost, and detours 50 blocks south to Washington Square before

reorienting and finally arriving at the Empire State Building. Is her displacement any different?

(a) ( , ) blocks

(b) Yes No

4.2 A treasure map you uncovered while vacationing on the Spanish Coast reads as follows: "If me treasure ye wants, me hoard

ye'll have, just follow thee directions these. Step to the south from Brisbain's Mouth, 5 paces through the trees. Then to the

west, 10 paces ye'll quest, with mud as deep as yer knees. Then 3 paces more north, and dig straight down in the Earth, and

me treasure, take it please." What is the displacement vector from Brisbain's Mouth to the spot on the Earth above the

treasure? Consider east the positive x direction and north the positive y direction.

( , ) paces

4.3 Write the vectors labeled A,B and C with

rectangular coordinates.

(a) A= ( , )

(b) B = ( , )

(c) C = ( , )

4.4 Consider these four vectors:

A goes from (0, 0) to (1, 2)

B from (1, í2) to (0, 2)

C from (í2, í1) to (í3, í3)

D from (í3, 1) to (í2, 3)

(a) Draw the vectors. Then answer the next two questions. (b) Which two vectors are equal? (c) Which vector is the negative

of the two equal vectors?

(a) Submit anwer on paper.

(b) i. A and B

ii. A and C

iii. A and D

iv. B and C

v. B and D

vi. C and D

(c) i. A

ii. B

iii. C

iv. D

Section 5 - Adding and subtracting vectors graphically

5.1 Draw each of the following pairs of vectors on a coordinate system, using separate coordinate systems for parts a and b of

the question. Then, on each coordinate system, also draw the vectors –B,A + B, and A – B. Label all your vectors.

(a) A = (0, 5);B = (3, 0)

(b) A = (4, 1);B = (2, –3)

5.2 The Moon's orbit around the Earth is nearly circular, with an average radius of 3.8×10^5 kilometers from the Earth's center. It

takes about 28 days for the Moon to complete one revolution around the Earth. (a) Put Earth at the origin of a coordinate

system, and draw labeled vectors to represent the moon's position at 0, 7, 14, 21 and 28 days. (b) On a separate coordinate

system, draw four labeled vectors representing the Moon's displacement from 0 days to 7 days, 7 days to 14 days, 14 days to

21 days, and 21 days to 28 days. (c) What is the sum of the four displacement vectors you drew in part "b"?

(^62) Copyright 2007 Kinetic Books Co. Chapter 3 Problems