Physics 114C Mechanics Lecture 8 Walker: 4'1

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Physics 114C - MechanicsLecture 8 (Walker
4.12)2D Motion BasicsApril 10, 2009

• John G. Cramer
• Professor of Physics
• B451 PAB
• cramer_at_phys.washington.edu

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Announcements

• Homework Assignment 2 is due at 1159 PM on
  Thursday, April 16.
• One week from today we will have Exam 1. It
  will have a 60 point multiple-choice part and two
  20 point free-response parts.
• You should have already obtained a H-ITT clicker
  from the U. Bookstore. RF Clickers should be set
  to Channel 02. Register your clicker using the
  Clicker link on the Physics 114B Syllabus page.
  So far 86/99 students have registered their
  clickers.
• My office hours are 1230-120 PM on Tuesdays and
  230-320 PM on Thursdays, both in the 114 area
  of the Physics Study Center on the Mezzanine
  floor of PAB A (this building).

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Lecture Schedule (Part 1)
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Two-Dimensional Kinematics
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Constant Velocity
If velocity is constant, motion is along a
straight line
A turtle walks from the origin at a speed of
v00.26 m/s and an angle of 250. In a time
t, the turtle moves through a straight line
distance of d v0t, with horizontal displacement
x d cos q and a vertical displacement y d
sin q. Equivalently, the turtles horizontal
and vertical velocity components arevx v0cos q
and vy v0sin q.
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Example The Eagle Descends
An eagle perchedon a tree limb 19.5 mabove
the water spotsa fish swimming nearthe surface.
He pushesoff the limb anddescends toward
thewater, maintaining aconstant speed of
3.20m/s at 20 below horizontal.

• How long does it take for the eagle to reach the
  water?
• How far has the eagle traveled horizontally when
  it reaches the water?

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Constant Acceleration in 2D
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Motion in Two Dimensions
Motion in the x- and y-directions should be
solved separately
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ExampleA Hummer Accelerates
A hummingbird is flying in such a way that
it is initially moving vertically with a speed of
4.6 m/s and accelerating horizontally at a
constant rate of 11 m/s2. Find the horizontal and
vertical distance through which it moves in 0.55
s.
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Projectile MotionBasic Equations

• Assumptions
• Ignore air resistance
• Use g 9.81 m/s2, downward
• Ignore the Earths rotation
• If the x-axis is horizontal and the y-axis points
  upward, the acceleration in the x-direction is
  zero and the acceleration in the y-direction is
  -9.81 m/s2

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Constant Acceleration withax 0 and ay -g
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Projectile MotionBasic Equations
The acceleration is independent of the direction
of the velocity
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Independence of Vertical and Horizontal Motion
When you drop a ball while walking, running,
or skating with constant velocity, it appears to
you to drop straight down from thew point where
you released it. To a person at rest, the ball
follows a curved path that combines horizontal
and vertical motions.
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Two divers run horizontally off the edge of
a vertical cliff. Diver 2 runs with twice the
speed of Diver 1. When they reach the surface of
the water below, how are the horizontal distances
xi that each diver covers related?
Clicker Question 1

• x1 x2
• 2x1 x2
• x1 2x2
• 4x1 x2
• x1 4x2

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Projectile Motionin Vector Form
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Graphs of x-y and v-t
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ExampleCanoeing on the Lake
Two canoeists start paddling at the same
time and head toward a small island 1 km north
in a lake. Canoeist 1 paddles at 1.35 m/s at an
angle of 450 north of east and Canoeist 2 starts
on the opposite shore, a distance of 1.5 km from
Canoeist 1. (a) At what angle q2 relative to
north must Canoeist 2 paddle to reach the
island? (b) At what speed must Canoeist 2 have,
if the canoes are to reach the island at the same
time?
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Example Cliff Diving

• Two boys, George and Sam, divefrom a
  high overhanging cliff intoa lake below.
• George (1) drops straight down.
• Sam (2) runs horizontally anddives outward.
• If they leave the cliff at the same time,which
  boy reaches the water first?
• (b) Which boy hits the water with the greater
  speed?

Since the vertical motion determines the time
required to reach the water, both boys reach the
water at the same.
George reaches the water with only a vertical
velocity, but Sam reaches the water with both
horizontal and vertical velocity components. The
vertical velocities are the same for both, so
Sams speed on entering the water is greater than
that of George.
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Example Electron in Motion
An electron in a cathode ray tube is
traveling with a horizontal speed of 2.10 x 109
cm/s when it enters the gap between deflection
plates that give it an upward acceleration of
5.30 x 1017 cm/s2. (a) How long does it take for
the electron to cover a distance of 6.20 cm? (b)
What is the vertical displacement during this
time?
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Example Jumping a Crevasse
A mountain climber encounters a crevasse in
an ice field. The opposite side of the crevasse
is 2.75 m lower, and the horizontal gap is 4.10
m. To cross the crevasse, the climber gets a
running start and jumps horizontally. (a) What
is the minimum speed v0 needed for the climber to
cross the crevasse? (b) Suppose the climber
jumps at 6.0 m/s, where does he land? (c) What
is his speed on landing?
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End of Lecture 8

• Before the next lecture on Monday, read Walker,
  Chapter 4.3-5
• Homework Assignment 2 should be submitted using
  the Tycho system by 1159 PM on Thursday, April
  16.(24 hours late Þ 70 credit)