# Kinematics - RMC Science Kinematics The Component Method Recall Vectors are quantities that have both magnitude and direction. Graphically, their sum is calculated by adding the vectors tip-to-tail. Graphical method is efficient for co-linear vectors and vectors problems with two vectors only. What if there are more? The component method! The Component Method Method that resolves each vector into its xcomponents and y-components.

The resultant is calculated through the addition of these components. Example #1 Determine the resultant of the following vectors using the component method: * a 10m[W 25 N ] * b 15m[ E 30 S ] Solution Vector a: X-component ay ax b:

a cos 25 x a * a x 10 cos 25 10m 250 300 bx by 15m * r * bx 15 cos 30 rx 10 cos 25 15 cos 30 * rx 3.93m | r | 3.27 2 3.93 2 * | r |

5.11m 3.93m * r Y-component ay sin 25 a * a y 10 sin 25 3.27m * b y 15 sin 30 ry 10 sin 25 15 sin 30 * ry 3.27 m 3.27 tan 1 3

. 93 39.76 0 * r 5.11m [ E 39.76 0 S ] Example #2 Determine the resultant of the following vectors using the component method: * a 10km[ N 30 W ] * b 20km[W 30 S ] * c 30km[ E 45 N ] Solution Vector a: b:

X-component ax ay 10km by 300 bx 300 20km c: 30km 450 cy Y-component a sin 30 x a * a x 10 sin 30 * a y 10 cos 30

bx 20 cos 30 * b y 20 sin 30 * c x 30 cos 45 * c y 30 sin 45 cx * r rx 10 sin 30 20 cos 30 30 cos 45 * rx 1.11 ry 10 cos 30 20 sin 30 30 sin 45 * ry 19.87

| r | 19.87 2 1.112 * | r | 19.90km 19.87 km * r 1.11km 19.87 tan 1 1.11 86.80 0 * r 19.90km [W 86.80 0 N ]