PHYS1006 Lecture Notes - Lecture 3: Resultant Force, Pythagorean Theorem, Projectile Motion
25 Jun 2018
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Chapter 3 Vectors and Projectile Motion
Physical Quantities:
Scalar: Magnitude only, eg. Distance, speed, mass.
Vector: Magnitude AND direction, eg. Displacement, velocity, force.
Addition of Vectors in one Dimension
Simply add or subtract the vectors according to their direction.
Example:
a) A person is walking along the ‘x’ direction as shown in the diagram. What is the
displacement of the person?
Displacement = 8km + 6km
Displacement = 14km towards east
b) A person is walking along the ‘x’ direction as shown in
the diagram. What is the displacement of the person?
Displacement = 8km + (-6)km
Displacement = 2km towards east
Addition of Vectors in two dimensions
Vectors can be added by two methods:
1. Graphical method using a ruler and protractor.
2. Analytical method or component method using trigonometry.
Subtraction of Vectors
Vector subtraction is a special case of vector addition.
V1 – V2 = V1 + (-V2)
Example
Two vectors A and B, whose magnitudes are A = 8.31 units and B = 5.55 units are shown in the
diagram.
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a) Find C = A + B
C = 8.31 + (-5.55)
C = 2.76 units in the + x direction
b) Find C = A – B
C = 8.31 – (-5.55)
C = 8.31 + 5.55
C = 13.86 units in the + x direction
c) Find C = B – A
C = -5.55 – (+8.31)
C = -13.86
C = 13.86 units in the –x direction
Multiplication of a vector by a scalar
A vector can be multiplied by a scalar c; the result a vector cV that has the same direction but a
magnitude of cV. If c is negative, the resultant vector points in the opposite direction.
Rectangular Components of a Vector
Any vector can be expressed as the sum of the other two vectors, which are called components.
Usually the other vectors are chosen to that they are perpendicular to each other.
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Pythagoras Theorem:
Example
If V = 10m/s-1 and = 60 find the x and y components of the vector V.
We can check the answers by substituting and into Pythagoras theorem.
Adding vectors by components
The components are effectively one-dimensional, so they can be added arithmetically:
Example
The figure below shows a box being pulled by two students, each exerting a force of 100N on the
box. What is the resultant force on the box?
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