chaney (glc568) – Vectors and 2D Motion – murthy – (21118)
1
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printout
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have
50
questions.
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before answering.
001
10.0 points
Which of the following are scalar quantities,
which are vector quantities?
a) velocity.
b) age.
c) speed.
d) acceleration.
e) temperature.
1.
Vector: velocity; Scalars: age, tempera
ture, speed, acceleration
2.
All are vectors.
3.
Vectors:
velocity, acceleration; Scalars:
age, temperature, speed
correct
4.
Vectors:
age,
temperature,
speed;
Scalars: velocity, acceleration
5.
All are scalars.
Explanation:
Speed is a measure of how fast something
moves, measured by a unit of distance divided
by a unit of time; a scalar quantity. Velocity
is specified by describing both speed and the
direction of motion; a vector quantity.
Age
is a measure of how long something exists;
a scalar quantity.
Acceleration is defined as
changes in velocity divided by a certain time
interval; a vector quantity since velocity is a
vector quantity. Temperature is the quantity
that tells how warm or cold an object is with
respect to some standard; a scalar.
002
10.0 points
Two airplanes leave an airport at the same
time.
The velocity of the first airplane is
750 m
/
h at a heading of 52
.
5
◦
. The velocity
of the second is 580 m
/
h at a heading of 90
◦
.
How far apart are they after 1
.
3 h?
Correct answer: 593
.
863 m.
Explanation:
Let :
v
1
= 750 m
/
h
,
θ
1
= 52
.
5
◦
,
v
2
= 580 m
/
h
,
and
θ
2
= 90
◦
.
Under constant velocity, the displacement
for each plane in the time
t
is
d
=
v t.
These displacements form two sides of a tri
angle with the angle
α
=
θ
2
−
θ
1
= 37
.
5
◦
between them. The law of cosines applies for
‘SAS’, so the distance between the planes is
d
=
radicalBig
d
2
1
+
d
2
2
−
2
d
1
d
2
cos
α .
Since
2
d
1
d
2
cos
α
= 2 (975 m) (754 m) cos 37
.
5
◦
= 1
.
16647
×
10
6
m
2
,
then
d
=
bracketleftbig
(975 m)
2
+ (754 m)
2
−
1
.
16647
×
10
6
m
2
bracketrightbig
1
/
2
= 593
.
863 m
.
003
10.0 points
A vector of magnitude 3 CANNOT be added
to a vector of magnitude 4 so that the magni
tude of the resultant is
1.
3.
2.
1.
3.
5.
4.
0.
correct
5.
7.
Explanation:
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chaney (glc568) – Vectors and 2D Motion – murthy – (21118)
2
The smallest magnitude of the resultant
occurs
when
the
vectors
are
antiparallel
(
R
= 1); the largest occurs when they are
parallel (
R
= 7).
Therefore all listed values
are possible except
R
= 0.
004
(part 1 of 2) 10.0 points
Two points in the
xy
plane have cartesian
coordinates (
x
1
, y
1
) and (
x
2
, y
2
), where
x
1
=
7
.
2 m,
y
1
=
−
10 m,
x
2
=
−
10 m, and
y
2
=
4
.
5 m.
Determine
the
distance
between
these
points.
Correct answer: 22
.
4964 m.
Explanation:
By simple geometry of triangle, the dis
tance between two points is
d
=
radicalBig
[
x
2
−
x
1
]
2
+ [
y
2
−
y
1
]
2
=
braceleftbigg
bracketleftBig
(
−
10 m)
−
(7
.
2 m)
bracketrightBig
2
+
bracketleftBig
(4
.
5 m)
−
(
−
10 m)
bracketrightBig
2
bracerightbigg
1
/
2
= 22
.
4964 m
.
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 Spring '08
 MURTHY
 Acceleration, Correct Answer, Chaney

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