Transcript Lecture 7 Wednesday Sept 10x

Lecture 7
Chapter 3: Vectors
Chapter 3
Vectors and Motion in Two Dimensions
Topics:
• Vectors, coordinate systems,
and components
•
•
Projectile motion
Circular motion
Sample question:
The archer fish shoots a stream of
water droplets at an insect. What
determines the path that the droplets
take through the air?
Slide 3-1
Looking Back: What You Already Know
From this class:
•
In Chapter 1 you learned what a vector is and learned how to
add vectors.
•
In Chapter 2 you learned about motion in one dimension.
Motion in two dimensions will build naturally on this foundation.
From previous classes:
•
You probably know that any two objects in free fall will undergo
similar motions; if you drop two objects from the same height at
the same time, they will hit the ground simultaneously.
•
You might well have learned a bit about vectors in another
course.
Slide 3-2
The acceleration of a particle in
projectile motion
1.points along the path
of the particle.
2. Is directed
horizontally
3. vanishes at the
particle’s highest
point.
4. is directed down at all
times.
5. Is zero.
1.
po
in
ts
a
lo
ng
2.
th
Is
ep
di
re
at
ct
h
e
..
3.
d
va
ho
ni
riz
sh
on
es
ta
at
lly
4.
th
is
ep
di
ar
re
tic
ct
ed
l..
.
do
wn
at
al
l. .
.
5.
Is
ze
ro
.
20% 20% 20% 20% 20%
Vectors
Slide 3-9
Vector addition—graphical method
A
C=A+B
B
Vector subtraction—graphical method
A
-B
D=A-B
-B
A
B
Representing a vector (2-dimensions)
Need magnitude (length) and direction
y
A
θ
Length = |A| =
magnitude of A
x
Multiplication by a scalar
What is a scalar? A number
B = cA
y
B = 3A
A
x
Special Cases
• Multiply by c = -1, reverses direction of vector
(1) A   A
• Multiply by c = 0, result is the zero vector
0A  0
Checking Understanding
An arrow is launched vertically upward. It moves straight up to a
maximum height, then falls to the ground. The trajectory of the
arrow is noted. Which graph best represents the vertical velocity of
the arrow as a function of time? Ignore air resistance; the only force
acting is gravity.
Slide 2-28
Answer
An arrow is launched vertically upward. It moves straight up to a
maximum height, then falls to the ground. The trajectory of the
arrow is noted. Which graph best represents the vertical velocity of
the arrow as a function of time? Ignore air resistance; the only force
acting is gravity.
Slide 2-29
The figure below shows five arrows with differing masses that were
launched straight up with the noted speeds. Rank the arrows, from
greatest to least, on the basis of the maximum height the arrows
reach. Ignore air resistance; the only force acting is gravity.
Slide 2-30
Problem
• Spud Webb, height 5'7", was one of the
shortest basketball players to play in the
NBA. But he had an impressive vertical
leap; he was reputedly able to jump 110
cm off the ground. To jump this high, with
what speed would he leave the ground?
Problem
• A football is punted straight up into the air;
it hits the ground
5.2 s later. What was the greatest height
reached by the ball?
With what speed did it leave the kicker’s
foot?
Problem
• Passengers on The Giant Drop, a free-fall
ride at Six Flags Great America, sit in cars
that are raised to the top of a tower. The cars
are then released for 2.6 s of free fall. How
fast are the passengers moving at the end of
this speeding up phase of the ride? If the cars
in which they ride then come to rest in a time
of 1.0 s, what is acceleration (magnitude and
direction) of this slowing down phase of the
ride? Given these numbers, what is the
minimum possible height of the tower?
Additional Clicker Questions
Mike jumps out of a tree and lands on a trampoline. The
trampoline sags 2 feet before launching Mike back into the air.
At the very bottom, where the sag is the greatest, Mike’s
acceleration is:
A. Upward
B. Downward
C. Zero
Slide 2-36
Homework Friday
– Reading: 3: 2-3 Vector components
– Problems: 2: 23, 28, 29, 31, 33, 48, 52; 3: CQ1, 1