Math 1320-6 Lab 7
Name:
A ns r
V
T.A.: Kyle Steffen
10 March 2016
uNID:
Instructions and due date:
• Due: 24 March 2016 at the start of class.
• For full credit: Show all of your work. and simplify your final answers.
• \Vork together! However, your work should be your own (ilot copied
from a group member).
Lah7
Math 1320-6
-
Page 2 of 5
1. This question is an application of vector addition:
The call sign for the airplane that carries the President of the IJuitecl States is ‘Air Force One”
(AFO). It has a cruising speed of around 925 km h’.
At one point in time during a flight from Washington, DC to Los Angeles, California, suppose
that: a) the heading of AFO was due west, b) its speed was 90% of its cruising speed, and c)
.
1
the wind was due north with a speed of 25 m s
(Note: The “heading” of an aircraft refers to the direction
thus the direction of its motion if there were no winds.)
in
which its nose is pointing, and
(a) Draw a sketch of the three vectors: i.) the velocity of AFO if there were no wind: ii.) the
wind velocity; and iii.) the resultant vector, which gives the velocity of AFO as seen by a
stationary observer on the ground. Also: What is the resultant vector in component form?
C)
NVik
€sV(I1&yi1
‘i’er
>Et
V
(tJ
VVifti V9t’i.
— (oq)(25 jC
- (25)
AEo
Qortvr+
b
(b) What direction and speed was AFO moving at that point
t—--
I. 5,
in til
ct= Vc7H
9
=-
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.
Math 1320-6
Lab7 -Page3of5
2. Consider the following four vectors: a
(1. 1). b
=
(1, —1). v
=
(—3.4). and w
(i.y).
(a) Compute PJa v (the projection of v onto a) and projb V. State your answers in component
form.
‘ (1
,2 ‘i (4 \ j
_1/4-)
1
V CL
I>
S
—
—
\JI
j
(.____
rd1V
.=
I
-
-
.—
._
L
4
[fT
(
Z’t’
(bJ
) ()
(4)
(- j)
F
—
-<‘Lt>
(b) Compute proja w and projb w. State your answers in component form.
---
--
-——
-
i}i>
—-
--
jWzW (t-F(-I)<i-1
r
3
-()/2>
LK}
(c) Use your answers from part (b). and compute the following sum: proj w+proj w. Simplify
your answer.
2
=
K:
w
-
+
3
+
* - ->
—‘
/‘Z
J
ZE)
2 can be expressed as
(d) Your answer to part (c) suggests the following: any vector (x. y) in R
the sum of its projections onto two distinct vectors.” This is not always true. If we require
that the two distinct vectors have a non-zero angle between them, then it is always true.
For part (d): What is the angle between a and b?
L(i)
I
Z2
9
c,
oJ
t.
Math 1320-6
Lab 7
-
Page 4 of 5
3. Terry has under an hour to check her bag, get through airport security, and catch her flight. She
is speed walking to her airline’s front desk, and is pulling her 16 kg suitcase at a constant speed
of 1.8 ms
. (Assume that the suitcase is standing upright and does not lean at an angle.) She
1
puils on the handle with a force of 120 N at an angle of 38° (measured from the horizontal).
12 0 N
(a) Sketch a figure.
of lOOm.
(b) Calculate the work
Wr Jvrce
-
spkteQrm.rRt
iIii5c
(i2DL)(wo
V\J
w
‘—‘1
)
Q
q45.t3 Nryu
i3
0
4
Toiij
()
(
•1
Lab 7
Math 1320-6
-
Page 5 of 5
4. A crane boom is 30 in long, has a mass of 450 kg, and is supporting a load of 10 kN, as shown
in the two diagrams below.
Three forces acting on the boom generate torque at its pivot point: i.) the force due to gravity
(acting at the center of mass of the boom), ii.) the force due to the tension in the cable (acting
at the upper end of the boom). and iii.) the force due to the load (also acting at the upper end
of the boom).
The boom is stationary. which means:
due t.o the tension.’
torqiie
due to gravity + torque due to the load
(e L
z
r
Write down a siigfe equation which involveS
3
—
(a)
=
torque
-
-
the magnitude of the three torques.
(Hint: There should be exactly one unknown
variable in your equation --the magnitude of
the force due to the tension.)
I[ I i I
Sn(
1
q
(45o 0
0
4500 q
rE
F
I1si()
(I000o N)(3Orn) ‘y(4)
1
j.,,
/OOO. 30.
-
?
r
I ‘T I ; n(€r)
I)
C3
C)j
()
3 C’
n (22
+-
A ()
IL/
udc4
and
23°
0
(b) Solve the equation from part (a) to find the
magnitude of the tension in the cable (in New
tons).
r
= 450
(2z°)
)
J1
E—c/=2’)
C
—