I) (a) We will start with displacement, the straight line (as the crow of moving object starting from an initial location and arriving at a final location. Vector quantities will be written in bold face i.e. A. Consider the situation of an ant that travels east, i.e. along the x axis, for 8 cm then travels northeast, i.e. 45° from the x axis, for 11 cm. Represent each leg of this journey by a vector on your graph paper. Vectors are written as arrows with the direction going from the tail of the arrow to the head of the arrow and the length of the arrow proportional to the magnitude (size) of the vector. Indicate the first part of the journey by an arrow of length 8 cm whose tail starts at the origin of your graph and whose head is at 8 units along the positive x direction. Call this vector A which is the displacement of the first part of the ant's journey. Now starting at the head of A draw a vector B which represents the second part of the ant's journey. Where does the ant end up? Note that total i.e. net displacement of the ant is the arrow (vector) that starts with its tail at the origin and its head at the head of B. This arrow is the vector sum A + B. (b) If the ant first goes 3 times as far along the x axis as before, i.e. 24 cm we describe this by a vector C=3A. Thus if we multiply a vector by a scalar we change its length (its magnitude) by the scalar multiplier. Draw vector C at a different place on your graph paper than where you drew A. On your graph paper show where the ant now ends up after the first leg of its journey. The ant now goes on as before on the second part of its trip. Graphically find C + B. (c) Now consider that after going east for 8 cm the ant then goes in the opposite direction i.e. southwest, or 225° from the x axis for 11 cm. This new displacement is a vector which is -B and can be written as (-1)B. Thus we can define vector subtraction as the addition of A to (-1)B. Using your graph paper draw A - B.
I) (a) We will start with displacement, the straight line (as the crow of moving object starting from an initial location and arriving at a final location. Vector quantities will be written in bold face i.e. A. Consider the situation of an ant that travels east, i.e. along the x axis, for 8 cm then travels northeast, i.e. 45° from the x axis, for 11 cm. Represent each leg of this journey by a vector on your graph paper. Vectors are written as arrows with the direction going from the tail of the arrow to the head of the arrow and the length of the arrow proportional to the magnitude (size) of the vector. Indicate the first part of the journey by an arrow of length 8 cm whose tail starts at the origin of your graph and whose head is at 8 units along the positive x direction. Call this vector A which is the displacement of the first part of the ant's journey. Now starting at the head of A draw a vector B which represents the second part of the ant's journey. Where does the ant end up? Note that total i.e. net displacement of the ant is the arrow (vector) that starts with its tail at the origin and its head at the head of B. This arrow is the vector sum A + B. (b) If the ant first goes 3 times as far along the x axis as before, i.e. 24 cm we describe this by a vector C=3A. Thus if we multiply a vector by a scalar we change its length (its magnitude) by the scalar multiplier. Draw vector C at a different place on your graph paper than where you drew A. On your graph paper show where the ant now ends up after the first leg of its journey. The ant now goes on as before on the second part of its trip. Graphically find C + B. (c) Now consider that after going east for 8 cm the ant then goes in the opposite direction i.e. southwest, or 225° from the x axis for 11 cm. This new displacement is a vector which is -B and can be written as (-1)B. Thus we can define vector subtraction as the addition of A to (-1)B. Using your graph paper draw A - B.
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Transcribed Image Text:I) (a) We will start with displacement, the straight line (as the crow or airplane flies distance) covered by a
moving object starting from an initial location and arriving at a final location. Vector quantities will be written
in bold face i.e. A.
Consider the situation of an ant that travels east, i.e. along the x axis, for 8 cm then travels northeast, i.e. 45°
from the x axis, for 11 cm. Represent each leg of this journey by a vector on your graph paper.
Vectors are written as arrows with the direction going from the tail of the arrow to the head of the arrow and the
length of the arrow proportional to the magnitude (size) of the vector. Indicate the first part of the journey by an
arrow of length 8 cm whose tail starts at the origin of your graph and whose head is at 8 units along the positive
x direction. Call this vector A which is the displacement of the first part of the ant's journey. Now starting at the
head of A draw a vector B which represents the second part of the ant's journey. Where does the ant end up?
Note that total i.e. net displacement of the ant is the arrow (vector) that starts with its tail at the origin and its
head at the head of B. This arrow is the vector sum A + B.
(b) If the ant first goes 3 times as far along the x axis as before, i.e. 24 cm we describe this by a vector
C=3A. Thus if we multiply a vector by a scalar we change its length (its magnitude) by the scalar multiplier.
Draw vector C at a different place on your graph paper than where you drew A. On your graph paper show
where the ant now ends up after the first leg of its journey. The ant now goes on as before on the second part of
its trip. Graphically find C + B.
(c) Now consider that after going east for 8 cm the ant then goes in the opposite direction i.e. southwest,
or 225° from the x axis for 11 cm. This new displacement is a vector which is -B and can be written as (-1)B.
Thus we can define vector subtraction as the addition of A to (-1)B. Using your graph paper draw A - B.
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