PHYS 2211 Study Guide - Spring 2019, Comprehensive Final Exam Notes - Acceleration, Euclidean Vector, Triangle

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Unit 0 : Vectors
A vector is a value that has direction. All measurements made in other science courses have been scalar in that
only values are needed. Consider 20 grams, 98.6°F and 1.00 grams/cc. These are three examples of scalar values.
Sometime direction is important. Suppose that two cars collide while one is moving at 60 mph and the other is
moving at 59 mph. Is the crash critical? It depends on if the two cars meet head-on or if the faster car rear-ends the
slower car. Identical numbers before the collision but two totally different results. Direction must be considered in
many of the problems of physics.
A vector is a measurement that has a number and a direction. The number part of a vector is called
“magnitude”. You could say that it is the scalar part of the vector. The direction part is usually given as an angle. We
will investigate angles more in tomorrow’s lesson. For today, directions like forward, backwards and sideways will do.
Billy Bob and Jimmy Joe
Billy Bob owns a nice pickup truck. Jimmy Joe has a bunch of rotten eggs that he needs to get rid of. Billy Bob drives
his truck with Jimmy Joe in the back. They are going across town to the rival high school neighborhood for some “not
so bright” action. On the way across town, Billy Bob stops at a store for a six pack of his favorite highly caffeinated
beverage. It has been determined that Jimmy Joe can toss a raw egg at 80 mph on a day when the wind is calm.
Scenario #1
Billy Bob is driving down the street at 60 mph with Jimmy Joe in the back of the truck. Ahead is a hitchhiker (HH)
looking for a ride? Jimmy Joe throws three eggs at the hitchhiker while driving along the street.
The first throw is forward and parallel to the motion of the truck.
The second throw is sideways perpendicular to the motion of the truck.
The third toss is backwards, against the motion of the truck.
See the figure below:
Warning! Do not try this at home without adult supervision.
A) During the first throw that is forward, parallel to the direction of motion of the truck, the following are observed:
1. Billy Bob and Jimmy Joe see the egg move forward at _____ mph.
2. The hitchhiker sees the egg moving towards him at _____ mph.
B) During the second throw the egg is tossed sideways or perpendicular to the direction of motion of the truck. When
the egg velocity is perpendicular to the truck velocity the following are observed.
1. Billy Bob and Jimmy Joe see the egg move sideways at _____ mph.
2. The hitchhiker sees the egg moving at _____ mph at an angle of _____° from the forward direction.
C) During the third throw that is backwards, antiparallel to the direction of motion of the truck, the following are
observed:
1. Billy Bob and Jimmy Joe see the egg move backwards at _____ mph.
2. The hitchhiker sees the egg moving towards him at _____ mph.
From the above scenarios you should have learned several things. Fill in the blanks below.
1. A vector that describes speed and direction is called __________.
2. When two vectors are parallel they can be combined using _________.
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3. When two vectors are antiparallel they can be combined using _______.
4. When two vectors are perpendicular they can be combined using __________ to get the magnitude and using
__________ to find the direction.
Scenario #2
Due to the large consumption of caffeinated beverages, Billy Bob needs to find a restroom. He increases his truck’s
forward speed to 80 mph with Jimmy Joe still in the back of the pickup truck. A second hitchhiker is noticed between
Billy Bob’s truck and the nearest restroom. Jimmy Joe makes three new attempts to egg a hitchhiker.
D) During the first throw that is forward, parallel to the direction of motion of the truck, the following are observed:
1. Billy Bob and Jimmy Joe see the egg move forward at _____ mph.
2. The hitchhiker sees the egg moving towards him at _____ mph.
E) During the second throw the egg is tossed sideways or perpendicular to the direction of motion of the truck. When
the egg velocity is perpendicular to the truck velocity the following are observed.
1. Billy Bob and Jimmy Joe see the egg move sideways at _____ mph
2. The hitchhiker sees the egg moving at _____ mph at an angle of _____° from the forward direction.
F) During the third throw that is backwards, antiparallel to the direction of motion of the truck, the following are
observed:
1. Billy Bob and Jimmy Joe see the egg move backwards at _____ mph.
2. The hitchhiker sees the egg moving towards him at _____ mph.
Vector Addition
http://id.mind.net/~zona/mstm/physics/mechanics/vectors/componentAddition/componentAddition2.htm
In the previous lesson you learned how to combine vectors that are parallel, antiparallel and perpendicular. But what
if the vectors are not at nice angles? How do you combine vectors that are different by 70° or 135°? There are three
different approaches to solving problems of this nature. In today’s lesson you will learn how to combine coplanar
vectors using the method of components. Be sure that you know how to place your calculator in the degree
mode since you will work exclusively in degrees in this course
Directions of Angles
Angles in this course are described in two different planes.
Vertical angles are measured from a line that runs parallel to
the ground. Consider the figure standing in the diagram to the
right. The figure’s left hand points in the horizontal direction.
The right hand points at 40° below the horizontal. If something
points at 40° below the horizontal then it also is pointing at 50°
from the vertical direction.
For the hand that is pointing parallel to the ground we know that it is not pointing up or down but merely
sideways. We still have not completely described the direction. Is the hand pointing north or south or at some angle
between north and east or an angle between south and west?
How do we describe those directions?
Consider the two angles shown in the figure to the right. The
angles are shown as you would see them if sitting in a tree looking
down on the angles from above. The coordinate axes are all drawn
parallel to the ground and pointing along cardinal points of the
compass.
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