P2 Week 6
Relative Velocity and Dot Product
Sections 3.5 and 1.10
Review of Adding Vectors:
Graphically and Algebraically
Draw the vectors tip-to-tail
The resultant is drawn from
the origin of to the end of
A
the last vector
Measure the length of
R
and i
Physics 2
Vectors (II)
Coordinates
1-dimensional motion
our position is always described by one
number at any time: x(t)
x(t)
t
Coordinates
2-dimensional motion
our position is always described by two
numbers at any time: x(t), y(t)
x(t)
y(t)
t
t
Coordina
Week 7
Motion in Two Dimensions
Sections 3.1 3.3
Position and Displacement
The position of an
object is described !by
its position vector, r
The displacement of
the object is defined as
the change in its
position
!
! r " rf # ri
General Motion Ideas
In tw
P2 Tutorial: Week 6
November 1, 2011
1. Given two vectors = 3.0 + 4.0 and =
1
(1
2
1).
(a) Find the dot (scalar) product of the two vectors .
(b) Write and in the polar form of (length, polar angles ), then calculate the angle between
the two vectors.
(
Week 5 Tutorial Problems
13 , 56 , B
1. Given that vector A
4, 1 , C
1, 2 , and D
10 , 252 , compute the follow-
ing and present a graphical representation of the resultant vectors in terms of the original vectors.
(a) D
A
1i + 0 j
(b) B
D
(c) A
D
B
3i
1j
Physics 2
Tutorial 3
October 11, 2011
Problem 1 Car Race. Recently, the exotic sports car company Bugatti released a new model of their
famed Veyron after an American car company developed a production sports car with a higher top speed
than the previous
Sit in the seats assigned to your ID number
10146831
12411414
12535033
13143339
13514131
13821796
14118308
16889971
17784039
17978418
17992213
18195769
18617678
18875321
22405012
22646502
22668312
23205092
23621457
23752278
24078007
24332688
24832789
2486
Warm-up problem
Consider the following function:
a) Find the smallest x for which the curvature of f(x) is zero
A. 1
B. 3/4
C. 0
D. /2
E.
a) Determine the minimum value of the slope of f(x) to 2 sig. figs.
A. -0.50
B. -0.33
C. -0.21
D. -0.16
E. -0.10
War
P2 Quiz week 2
Problem 1 Doing the algebra
In lecture, I pointed out that
v2= (vo)2+2a(xxo) [3]
Could be obtained from
x= xo+vot+(1/2)at2 [1]
x= xo+ (1/2)(v+vo)t [2]
Do the algebra to
Quiz Question 1-Week 5
!
S u p p o s e v e lo c ity o f o b je c t 1 is g iv e n b y v e c to r v 1
w h ic h h a s m a g n itu d e 3 a n d d ir e c tio n + 3 0 d e g r e e s ,
a n d o b je c t 2 h a s v e lo c ity v e c to r v 2 w ith m a g n itu d e
3 a
Physics 2 Tutorial: Week 2
1. Regions outside of sunny Southern California experience a strange phenomenon known as thunderstorms.
A good way to estimate the distance between you and the storm is to count in 5-second
intervals between when you see the ash
Week 4 Tutorial Solutions
1.) Computethefollowing.Thenevaluatetheresultat
0 .Notethatweareusing
asa
variablename.
1
sin sin
2
1
sin cos
cos sin
2
cos
1
sin
2
cos cos
2
cos
Evaluatedat
0
or
2.) Ahungryanteaterislookingtozotits
Quiz Problem 2- Week 7- Basic
If a missile is launched at 30 degrees
from vertical from the edge of a cliff
with a speed of 40 m/s,
1) what direction with respect to
horizontal is it traveling after 4s?
2) what is the position vector at 4s if
the origin i
Physics 2
Quiz week 3
Problem 1
1) A student throws a set of keys vertically upward
to her sorority sister, who is in a window 4.00 m
above. The keys are caught 1.50 s later by the sister's
outstretched hand.
(a) With what initial velocity were the keys t
P2 Quiz 1
(1) Exercise is good for you
An UCI student keeps t by bicycling and running every
day. On Monday, she spends 30 minutes on each
acKvity and covers a total of 12 miles. On Tuesday, she
runs for
Physics 2, Tutorial 8
1. Aint it great. Integrate the following over the variable x (all symbols other than x are assumed
to be constants) unless the explicit integral is given:
a.
i. Solution:
b.
i. Solution: ln(x + a)
c.
i. Solution: -1/x
d.
i. Solution
Quiz- Week 8 Problem 1
At a future X-games event, a motorcycle rider want to jump across 30
cars stacked side by side. Each car is 1 m wide. The platform is 10m
above the ground. The motorcycle is equipped with a rocket that
provides horizontal accelerati
5.) Aballisdroppedfromaheight above
theground.Howlongdoesittaketofall
totheground?
Physics 2 Practice Exam
PartA
a.)
1.) Findthescalarproductofthefollowing
twovectors:
5,30 and
10,220
a.) 49
b.) 49answer
c.) 250
d.) 17
e.) 17
5 10 cos 220
c.)
d.)
30
2.
P2 Quiz Week 6
Quiz Week 6 Problem 1
A passenger train is traveling due west at 10 km/hr.
Rain is falling straight down at 20 km/hr. What is
the velocity vector, vrt , of the raindrops with
respect to an
P105 lecture 4
January 29, 2008
Somatoform Disorders Hypochondriasis 1. Preoccupation with fears or beliefs that one has a serious disease, based on misinterpretation of bodily symptoms, lasting at least six months 2. Persistence of preoccupation