PH 211 Winter 2014
Wednesday January 15
Homework 2 hand-in
There is one problem for set 2 (Chapter 1) to hand in. Because of the nature
of the problems, I cannot use the assigned problems in Mastering Physics, so I
assign problem 1.42 from the end of the chapter.
Hand in your written homework to box 12 on the second floor, before Friday
5pm. Make sure you write your name clearly on the top of the sheet!
This first problem is not meant to be difficult, my goal is to get everybody,
including the grader and myself, in the routine! For this problem, draw a
complete pictorial representation! Do not use any mathematics to get the
answer!
Ice hockey star Bruce Blades is 5.0 m from the blue line and gliding toward it
at a speed of 4.0 m/s. You are 20 m from the blue line, directly behind Bruce.
You want to pass the puck to Bruce. With what speed should you shoot the
puck down the ice so that it reaches Bruce exactly as he crosses the blue line?
Google moderator
Which topic would you like to discuss in class on
Friday?
http://www.google.com/moderator/#15/e=211
071&t=211071.40
Google moderator
Today’s questions:
http://www.google.com/moderator/#16/e=20e
0eb
Which of these plots shows a positive
velocity and a negative acceleration?
x
A
B
x
t
x
C
t
x
t
D
t
Which of these plots shows a positive
velocity and a negative acceleration?
A
B
C
D
86%
2%
D
C
6%
B
6%
A
A.
B.
C.
D.
In this x(t) plot at how many points in
time is the acceleration equal to zero?
In this x(t) plot at how many points in
time is the acceleration equal to zero?
A.
B.
C.
D.
E.
0
2
4
6
8
84%
5%
0
2%
2
4
5%
4%
6
8
In this x(t) plot at how many points in
time is the acceleration equal to zero?
Velocity large, positive
x
Velocity small, positive
x
t
t
x
t
x
x
Velocity
zero
t
Velocity large, negative
t
Velocity small, negative
Practice: draw v(t)
and a(t) for this graph
x
A
B C
D
E
t
Moe stands on a cliff with two balls. One is thrown straight up with
initial speed vo, the other is thrown straight down with the same
initial speed, vo. How do the final velocities of the two balls compare
right before they hit the ground? DRAW a motion diagram OR graph
to JUSTIFY your choice! (what assumptions are you making/model
are you using)
1. The ball thrown up is faster right before it hits the
ground
2. The ball thrown down is faster right before it hits
the ground
3. The two balls have the same speed right before
they hit the ground
4. There isn’t enough information to determine the
answer based on what is given
Moe stands on a cliff with two balls. One is thrown straight up
with initial speed vo, the other is thrown straight down with the
same initial speed, vo. How do the final velocities of the two
balls compare right before they hit the ground?
A.
67%
...
h
no
ug
’t
e
isn
er
e
Th
in
fo
r
sa
..
th
e
ve
ba
lls
o
w
et
Th
10%
ha
n
w
hr
o
lt
al
eb
Th
eb
al
lt
hr
o
w
n
up
do
w
is
n
is
fa
s
...
t. .
12% 10%
Th
The ball thrown up is faster
right before it hits the
ground
B. The ball thrown down is
faster right before it hits the
ground
C. The two balls have the
same speed right before
they hit the ground
D. There isn’t enough
information to determine
the answer based on what
is given
Asked to graph the velocity vs. time of a certain motion, a researcher
draws graph 1 below. Then he draws graph 2, showing the position vs.
time for the same motion.
• The researcher who drew the above graphs is 99% sure he drew
graph 2 correctly. Is there some way he can use his position graph to
check for inconsistencies with his velocity graph? If so, do it and
explain your reasoning.
• If asked to draw a velocity graph for motion someone just observed,
why might they first draw the position graph? (most experienced
people do this)
The graph shows position as a function
of time for two trains running on
parallel tracks. Which is true:
1. At time tB, both trains
have the same velocity.
2. Both trains speed up all
the time.
3. Both trains have the same
velocity at some time
before tB.
4. Somewhere on the graph,
both trains have the same
acceleration
The graph shows position as a function of time
for two trains running on parallel tracks. Which
is true:
A. At time tB, both trains
have the same velocity.
B. Both trains speed up all
the time.
C. Both trains have the
same velocity at some
time before tB.
D. Somewhere on the
graph, both trains have
the same acceleration
88%
8%
gr
a
sa
th
e
th
e
on
av
e
So
m
ew
he
re
sh
ain
tr
th
Bo
ph
.. .
m
l.
al
up
ed
ss
pe
ain
tr
th
Bo
...
..
.
sh
a.
ain
tr
ot
h
,b
tB
e
tim
At
4%
0%
Draw x(t) for a case where the
position and acceleration always
have opposite signs.
Average velocity.
𝑣𝑎𝑣𝑒𝑟𝑎𝑔𝑒
𝑟𝑓𝑖𝑛𝑎𝑙 − 𝑟𝑖𝑛𝑖𝑡𝑖𝑎𝑙
=
𝑡𝑓𝑖𝑛𝑎𝑙 − 𝑡𝑖𝑛𝑖𝑡𝑖𝑎𝑙
I drive from my house to another city 60 km
away in one hour, spend one hour having lunch
in that city, and drive back in one hour. How
large is the average velocity for the trip?
A.0 km/hour
B.20 km/hour
C.40 km/hour
D.60 km/hour
I drive from my house to another city 60 km
away in one hour, spend one hour having lunch
in that city, and drive back in one hour. How
large is the average velocity for the trip?
0 km/hour
20 km/hour
40 km/hour
60 km/hour
38%
ur
/h
o
km
60
40
km
/h
o
ur
7%
ur
/h
o
km
20
km
/h
ou
r
8%
0
A.
B.
C.
D.
47%
I drive from my house to another city 60 km
away in one hour, spend one hour having lunch
in that city, and drive back in one hour. How
large is the average speed for the trip?
A.0 km/hour
B.20 km/hour
C.40 km/hour
D.60 km/hour
I drive from my house to another city 60 km
away in one hour, spend one hour having lunch
in that city, and drive back in one hour. How
large is the average speed for the trip?
79%
0 km/hour
20 km/hour
40 km/hour
60 km/hour
13%
5%
ur
60
km
/h
o
ur
40
km
/h
o
ur
km
/h
o
20
km
/h
ou
r
3%
0
A.
B.
C.
D.
Average speed:
Total DISTANCE travelled divided by
total time!
Instantaneous velocity.
𝑟 𝑡 + ∆𝑡 − 𝑟 𝑡
𝑑𝑟
𝑣 𝑡 =
=
∆𝑡
𝑑𝑡
Instantaneous velocity.
𝑥 𝑡 = 𝑥 𝑡 𝑖 + 𝑦 𝑡 𝑗 + 𝑧(𝑡)𝑘
𝑑𝑥
𝑑𝑦
𝑑𝑧
𝑣 𝑡 =
𝑡 𝑖+
𝑡 𝑗+
(𝑡)𝑘
𝑑𝑡
𝑑𝑡
𝑑𝑡
Instantaneous velocity,
for computational folks.
𝑣 𝑡 =
𝑟 𝑡+
1
∆𝑡
2
− 𝑟 𝑡−
∆𝑡
1
∆𝑡
2
𝑑𝑟
=
𝑑𝑡