Chapter 3
Two Dimensional Motion and Vectors
Introduction to Vectors
Scalers:-
Has magnitude ONLY
Ex: speed ,mass,temp,distance,volume
Vectors:-
have both magnitude and direction
Ex: acceleration, velocity, displacement
Vectors are also represented by arrows.
the length of a vector arrow represents the magnitude of the vector.
The arrow shows the direction
- The longer the arrow the more magnitude the vector has.
- A vector remains unchanged only if it is moved parallel to its original direction
- Multiplying or dividing vectors by scalars results in vectors
- if vectors are moved according to the rules of the triangle method of vector addition, then the
resultant vector is drawn from the tail of the first vector to the tip of the last vector.
Vectors can be added graphically
1. draw vectors head to tail (maintain length and direction)
2. using a straight edge, draw the resultant vector beginning at the tail of the first vector and ending
at the head of the last vector.
3. using the same scale as the added vectors, determine the magnitude and direction of the resultant
vector.
Vector operations
The projection of a vector along the axes of a coordinate system is called a component of the vector
The components of a vector are perpendicular.
If the x-component of B equals the magnitude of B, then By equals zero.
Finding resultant
1.Break components and find x and y
Sine θ = opposite/hypotenuse Y/R
Cosine θ = adjacent/hypotenuse X/R
2.Get total x and total y
3.Use Pythagorean to find resultant a2 + b2 = c2
4.Find Tangent θ = opposite/adjacent total y / total x
Projectile motion
Projectiles are objects thrown or launched into the air.
Projectile motion : a curved path an object follows when thrown, launched, projected
Ex; a punted football , a thrown baseball , a water droplet cascading down a waterfall
- in the absence of air resistance, the path of a projectile is a parabola
- with air resistance, path is shortened
- For an object to be a projectile, it must be in free fall and its initial velocity must have a horizontal
component.
- the motion of a projectile in free fall is characterized by v x =constant and ay = -g.
- Assuming no air friction and ay = -g, the horizontal displacement of a projectile depends on the
vertical component and the horizontal component of its initial velocity.
Two Dimensional Motion and Vectors
Introduction to Vectors
Scalers:-
Has magnitude ONLY
Ex: speed ,mass,temp,distance,volume
Vectors:-
have both magnitude and direction
Ex: acceleration, velocity, displacement
Vectors are also represented by arrows.
the length of a vector arrow represents the magnitude of the vector.
The arrow shows the direction
- The longer the arrow the more magnitude the vector has.
- A vector remains unchanged only if it is moved parallel to its original direction
- Multiplying or dividing vectors by scalars results in vectors
- if vectors are moved according to the rules of the triangle method of vector addition, then the
resultant vector is drawn from the tail of the first vector to the tip of the last vector.
Vectors can be added graphically
1. draw vectors head to tail (maintain length and direction)
2. using a straight edge, draw the resultant vector beginning at the tail of the first vector and ending
at the head of the last vector.
3. using the same scale as the added vectors, determine the magnitude and direction of the resultant
vector.
Vector operations
The projection of a vector along the axes of a coordinate system is called a component of the vector
The components of a vector are perpendicular.
If the x-component of B equals the magnitude of B, then By equals zero.
Finding resultant
1.Break components and find x and y
Sine θ = opposite/hypotenuse Y/R
Cosine θ = adjacent/hypotenuse X/R
2.Get total x and total y
3.Use Pythagorean to find resultant a2 + b2 = c2
4.Find Tangent θ = opposite/adjacent total y / total x
Projectile motion
Projectiles are objects thrown or launched into the air.
Projectile motion : a curved path an object follows when thrown, launched, projected
Ex; a punted football , a thrown baseball , a water droplet cascading down a waterfall
- in the absence of air resistance, the path of a projectile is a parabola
- with air resistance, path is shortened
- For an object to be a projectile, it must be in free fall and its initial velocity must have a horizontal
component.
- the motion of a projectile in free fall is characterized by v x =constant and ay = -g.
- Assuming no air friction and ay = -g, the horizontal displacement of a projectile depends on the
vertical component and the horizontal component of its initial velocity.
