PHY2053 RECITATIONS, SPRING 2011
Recitation 3 (Chapter 3) Jan. 31Feb. 4
Ch. 3 # 2.
A jetliner is moving at a speed of 245 m/s. The vertical component of the plane’s velocity
is 40.6 m/s. Determine the magnitude of the horizontal component of the plane’s velocity.
REASONING AND SOLUTION
The horizontal and vertical components of the plane's velocity
are related to the speed of the plane by the Pythagorean theorem:
2
2
2
h
v
v
v
v
=
+
.
Solving for
v
h
we
have
v
v
v
h
v
2
2
2
(245 m / s)
40.6 m / s)
242 m / s
=

=

=
2
(
Ch. 3 # 8.
In a mall, a shopper rides up an escalator between floors. At the top of the escalator, the
shopper turns right and walks 9.00 m to a store. The magnitude of the shopper’s displacement from
the bottom of the escalator to the store is 16.0 m. The vertical distance between the floors is 6.00 m.
At what angle is the escalator inclined above the horizontal?
REASONING
Consider first the shopper’s ride up the escalator. Let the diagonal length of the
escalator be
L
, the height of the upper floor be
H
, and the angle that the escalator makes with
respect to the horizontal be
θ
(see the diagram). Because
L
is the hypotenuse of the right triangle
and
H
is opposite the angle
θ
, the three quantities are related by the inverse sine function:
1
1
o
sin
sin
h
H
h
L
θ


=
=
(1.4)
Now consider the entire trip from the bottom to the
top of the escalator (a distance
L
), and then from the
top of the escalator to the store entrance (a distance
s
). The right turn between these two parts of the trip
means that they are perpendicular (see the diagram).
The shopper’s total displacement has a magnitude
D
,
and this serves as the hypotenuse of a right triangle
with
L
and
s
. From the Pythagorean theorem, the three sides are related as follows:
2
2
2
D
L
s
=
+
.
SOLUTION
Solving
2
2
2
D
L
s
=
+
for the length
L
of the escalator gives
2
2
L
D
s
=

.
We now use this result and the relation
1
sin
H
L
θ

=
to obtain the angle
θ
:
(
29
(
29
1
1
1
2
2
2
2
6.00 m
sin
sin
sin
27.0
16.0 m
9.00 m
H
H
L
D
s
θ



=
=
=
=


o
1
θ
s
Entire view
Up the escalator
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Ch. 3 # 16.
A skateboarder shoots off a ramp with a velocity of 6.6 m/s, directed at an angle of 58°
above the horizontal. The end of the ramp is 1.2 m above the ground. Let the
x
axis be parallel to
the ground, the +
y
direction be vertically upward, and take as the origin the point on the ground
directly below the top of the ramp.
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 Spring '09
 Staff
 Pythagorean Theorem, Acceleration, Velocity, m/s, Euclidean geometry

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