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PHYS 121 Homework 2
Due:
29 January 2007
Problem 1.
(i)
Consider two arbitrary nonzero vectors
±a
and
±
b
and a third vector constructed from the diﬀerence of
them,
±
c
=
±a

±
b
. State whether the following statements can be true or not and brieﬂy justify your
answers: (1)
c > a
, (2)
c > a
and
c > b
, (3)
c
=
a
+
b
, and (4)
c > a
+
b
. [
Note
: Recall that
c
≡ 
±
c

.]
(ii)
You throw a ball upward at some angle. After some time you measure the velocity of the ball to
be
±v
= (15ˆ
ı

2
.
5ˆ
) m
/
s. Did you measure the velocity when the ball was on the way up or the
way down? [
Note
: Assume the standard coordinate system where
x
is positive to the right and
y
is
positive upward.]
(iii)
Question 4.3.
(iv)
A projectile is launched with an initial velocity,
±v
0
=
v
0
,x
ˆ
ı
+
v
0
,y
ˆ
. What is the velocity of the
projectile when it reaches the top of its trajectory,
±v
top
? What is the acceleration of the projectile
when it reaches the top of its trajectory,
±a
top
?
(v)
Is it possible to accelerate while moving at a constant speed?
(vi)
Is it possible to accelerate while moving at a constant velocity?
Problem 2.
(i)
Problem 3.4.
(ii)
A vector has a magnitude of 8
.
0 m and points at 130
◦
as measured from the
x
axis. Write this vector
in unit vector notation.
Problem 3.
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 Spring '08
 kernan
 mechanics, Work

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