1. Vectors

2. A vector is a quantity and direction of a
variable, such as; displacement, velocity,
acceleration and force.
A vector is represented graphically as
an arrow. The length represents the
magnitude (quantity) of the vector, the angle
shows the direction.

3. Vectors can be multiplied or divided by a scalar.
A scalar is a value with no direction
If A = 5 m
then 2A is:
(10 m)

4. Vectors can be added to find the “net” resultant
Connect vectors “tip to tail”
A + B B A

5. To find the direction of the vector, use trig. functions
To find the magnitude of the resultant vector, use the Pythagorean Theorem
a2 + b2 = c2
To find the direction of the vector, use trig. functions
tanq = opp/adj sinq = opp/hyp
cosq = adj/hyp

6. direction: tanq = opp/adj = 1.5 m/s2 / 6 m/s2 = .25
magnitude: c2 = a2 + b2
= (6 m/s2)2 + (1.5 m/s2)2
c = 6.18 m/s2
direction: tanq = opp/adj
= 1.5 m/s2 / 6 m/s2
= .25
q = tan-1 (.25)
= 14°

7. Measure all directions from the positive x-axis
If no logical “x-axis” exists, explain your
coordinate system. (i.e.: 20° ahead of down
the field)

8. A vector can be broken down into its x and y
components
5 m
y comp
38°
x comp
cos 38° = x comp / 5 m
x = (5 m) cos38°
= 3.94 m
y = (5 m) sin38° = 3.08 m

9. You can add vectors that are not perpendicular by adding their x and y components to make a right triangle, and find the resultant

10. x = 5 m(cos 75°) + 4 m(cos 25°) = 4.92 m y = 5 m(sin75°) + 4 m(sin25°)
magnitude2 = (4.92 m)2 + (6.52 m)2
mag = 8.17 m
direction: tanq = 6.52/4.92
q = 53°

11. Find the resultant vector’s magnitude and direction
76°
7.5 N
19°
5 N
29°