Vectors

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.

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)

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

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

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°

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)

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

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

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°

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