9/11/2016
HW3
HW3
Due: 11:59pm on Saturday, September 10, 2016
You will receive no credit for items you complete after the assignment is due. Grading Policy
Problem 3.2
Part A
Find C ⃗ =
⃗ ⃗ A +B
.
ANSWER:
Part B
Find D⃗ =
⃗ ⃗ A −B
.
ANSWER:
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HW3
Problem 3.6
Find x­ and y­components of the following vectors.
Part A
∘
r ⃗ = (150m, 45
below positive x − axis)
Express your answers using two significant figures. Enter your answers numerically separated by a comma.
ANSWER:
rx
, ry = m Part B
∘
v ⃗ = (620m/s, 40
above positive x − axis)
Express your answers using two significant figures. Enter your answers numerically separated by a comma.
ANSWER:
vx
, v y = m/s Part C
2
a⃗ = (5.8m/s , negative y − direction)
Express your answers using two significant figures. Enter your answers numerically separated by a comma.
ANSWER:
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ax
HW3
, ay = m/s2 Problem 3.12
Let A⃗ =
2^
ı + 3^
ȷ
and B⃗ =
4^
ı − 2^
ȷ
.
Part A
Plot vectors A⃗ and B⃗ .
Draw the vectors with their tails at the origin.
ANSWER:
Part B
This question will be shown after you complete previous question(s).
Problem 3.16
Let A⃗ =
7^
ı − 3^
ȷ
, B⃗ =
−2 ^
ı + 6^
ȷ
, and F ⃗ =
⃗ ⃗ A − 4B
.
Part A
⃗ What is the component form of vector F ?
ANSWER:
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HW3
F ⃗ =
15 ^
ı − 27^
ȷ
F ⃗ =
9^
ı + 27^
ȷ
F ⃗ =
14 ^
ı − 15^
ȷ
F ⃗ =
−15 ^
ı + 27^
ȷ
Part B
⃗ What is the magnitude of vector F ?
ANSWER:
F
= Part C
⃗ What is the direction of vector F ?
ANSWER:
= ∘ below positive x­axis θ
Enhanced EOC: Problem 3.26
The figure shows vectors A⃗ and B⃗ . Find D⃗ = 2.70 A⃗ + B⃗ .
You may want to review (
page ) .
For help with math skills, you may want to review:
Vector Addition
Part A
Express D⃗ in the form Dx , Dy , where the x and y components are separated by a comma.
You did not open hints for this part.
ANSWER:
⃗ D
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HW3
Problem 3.02
Part A
Vectors A⃗ and B⃗ are shown in the figure. Vector C⃗ is given by C⃗ = B⃗ ­ A⃗ . The magnitude of vector A⃗ is 16.0 units,
and the magnitude of vector B⃗ is 7.00 units. What is the magnitude of vector C⃗ ?
ANSWER:
17.5
16.2
15.5
9.00
9.53
Problem 3.42
The figure shows three ropes tied together in a knot. One of your
friends pulls on a rope with 3.0 units of force and another pulls on
a second rope with 5.0 units of force.
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HW3
Part A
How hard must you pull on the third rope to keep the knot from moving?
ANSWER:
F
= units of force Part B
In what direction must you pull on the third rope to keep the knot from moving?
ANSWER:
= ∘ counterclockwise from the left direction θ
Problem 3.20
Part A
^
⃗ ^
⃗ ⃗ ^
^
If A⃗ = + 3 ^i ­ 2 ^
j ­ 4 k and C = ­ 5 i ­2 j ­ 3 k , which of the following numbers is closest to the magnitude of A ­ C?
ANSWER:
6
12
8
11
10
Problem 3.32
Jim's dog Sparky runs 45 m northeast to a tree, then 70 m west to a second tree, and finally 20 m south to a third tree.
Part A
Calculate Sparky's net displacement vector.
Enter the east and north components of the net displacement, separated by commas.
ANSWER:
⃗ (Dnet )
East
,(D⃗ net )North = m Part B
Calculate the magnitude of Sparky's net displacement.
Express your answer in meters.
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HW3
ANSWER:
Dnet
= m Part C
Calculate the direction of Sparky's net displacement.
Express your answer in degrees.
ANSWER:
θnet
= ∘ north of west Problem 3.16
Part A
Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as
shown in the figure. If the forces have magnitudes F1 = 1.0 N, F2 = 14.0 N and F3 = 13.0 N, where N is the standard
unit of force, what is the component of the net force F⃗ net
⃗ ⃗ ⃗ =F +F2 + F3
parallel to the floor?
ANSWER:
5.5 N
10 N
12 N
15 N
Problem 3.12
Part A
The components of vector A⃗ are A x = +8.7 and A y = ­5.5 , and the components of vector B⃗ are given are Bx = ­4.3
and By = ­3.8. What is the magnitude of the vector B⃗ ­ A⃗ ?
ANSWER:
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HW3
10
16
18
13
8.5
Problem 3.20
⃗ ^
^
Let E⃗ = 3^i + 3^
j and F = 3 i − 3 j .
Part A
Find the magnitude of E⃗ .
ANSWER:
Part B
Find the magnitude of F .⃗ ANSWER:
Part C
Find the magnitude of E⃗ + F .⃗ ANSWER:
Part D
Find the magnitude of −E⃗ − 2F .⃗ ANSWER:
Conceptual Question 3.2
Part A
⃗ ⃗ ⃗ https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4710744
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HW3
If C ⃗ =
⃗ ⃗ A +B
, can C
= A+B
?
ANSWER:
Yes
No
Part B
Can C
> A+B
?
ANSWER:
Yes
No
Problem 3.08
Part A
Vector A⃗ has a magnitude of 5.5 cm and points along the x­axis. Vector B⃗ has a magnitude of 7.5 cm and points at
+30° above the negative x­axis.
(a) Determine the x and y components of Vector A⃗ .
Enter your answers numerically separated by a comma.
ANSWER:
Ax , A y = cm Part B
(b) Determine the x and y components of Vector B⃗ .
Enter your answers numerically separated by a comma.
ANSWER:
Bx , B y = cm Part C
(c) Determine x and y components of the sum of these two vectors.
Enter your answers numerically separated by a comma.
ANSWER:
Rx , R y = cm https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4710744
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HW3
Part D
(d) Determine the magnitude of the sum of these two vectors.
Enter your answer numerically.
ANSWER:
R
= cm Part E
(e) Determine the direction of the sum of these two vectors.
Enter your answer numerically.
ANSWER:
° above the negative x­axis Problem 3.34
Jack and Jill ran up the hill at 3.0 m/s . The horizontal component of Jill's velocity vector was 2.5 m/s .
Part A
What was the angle of the hill?
Express your answer in degrees.
ANSWER:
= θ
∘ Part B
What was the vertical component of Jill's velocity?
Express your answer with the appropriate units.
ANSWER:
vy
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