Transcript Chapter 3 VECTORS

Chapter 3 VECTORS
Goals: scalar vs vector, resultant, find
magnitude and direction, use the
Pythagorean Theorem, trig functions, and
kinematic equations (pg58) to calculate
projectile motion
How can motion in two directions be
determined? Section 3.1 Vectors
► Scalar-
magnitude no direction distance, time,
speed, volume
► Vector- magnitude and direction displacement,
velocity, acceleration
► Combination of two or more vectors
► Displacement or velocity
► Properties of vectors- magnitude and direction,
resultant, hypotenuse, add or subtract in any
order, subtraction adds the opposite and multiply
or divide by scalar is still a vector
How can magnitude and direction be
found? Section 3.2 Vector
Operations
► Graphically and Mathematically
► Graphically- 1.choose a scale 2.draw
vector 3.use
protractor and rule to draw next vector 4.measure
the resultant
► Practice Problems
► Mathematically- for vectors at right angles
use Pythagorean Theorem to calculate magnitude
and tanֿ1 to calculate angle of direction
c²=a²+b²
θ=tanֿ1
► Practice Problems
Is there another way to calculate
Vectors?
► If
the vector and its direction is known the vector
can be resolved into component velocities
► think of a right triangle
► vector = hypotenuse
► y-axis opp/hyp sin θ
► Vy= sinθ V
► x-axis adj/hyp cos θ
► Vx= cosθ V
► Practice Problems
How is Projectile Motion described?
Section 3.3 Projectile Motion
► Parabola
curved path of an object pushed but still under
the force of gravity
► acceleration in y direction = -9.81m/s²
► Two types: Horizontal and Launched
► Horizontal Projectile Motion has two components:
► Δx = Vx · t
Δy = ½ ay · t²
► Solve for t
t² y = 2y / ay t x = -2Vy/a t=x/v
►
What about launched objects?
Break the vector into Vx and Vy components and solve
the unknown using the equations for horizontal
projectiles
► Vy = sin θ · V
Vx = cos θ · V
► Δy = ½ ay · t²
Δx = Vx · t
►
x - variables
y – variables
►
Δx=
Δy= 0
►
Vi= (vector)
Vi= (vector)
►
Vx= component
Vy= component
►
ax= 0
ay= -9.81 m/s²
►
t = (same)
t = (same)
►
► We
studied VECTORS
► examples include:
► displacement
► velocity
► acceleration
► What other vector are we forced to study in
order to understand motion?
► Right!
► FORCE
► and I can’t wait!!!