Adding Vectors Example of adding two vectors neither
- Slides: 7
Adding Vectors Example of adding two vectors neither at right angles to one another nor on an x or y axis.
The Process: 4 First draw the vectors on an x: y axis, showing them 4 4 4 attached head to tail. Second, determine the x and y components of V 1. Third, determine the x and y components of V 2. Fourth, Add the x components of the vectors together. Fifth, Add the y components of the vectors together. Sixth, Use the sum of the x components as the x component of the resultant vector; Use the sum of the y components as the y component of the resultant vector. Seventh, proceed to “add” the resultant’s x and y values.
The Problem:
Resolve the 1 st vector into its x and y components. V 1 y = V 1 * Sin 60 or V 1 * Cos 30 = 0. 866 Km, N V 1 x = V 1 * Cos 60 or V 1 * Sin 30 = 0. 5 km, E
Resolve the 2 nd vector into its x and y components. V 2 y = V 2 * Sin 30 or V 2 * Cos 60 = 1 Km, N V 2 x = V 2 * Cos 30 or V 2 * Sin 60 = 1. 732 Km, E
Next, add the components. V 1 y + V 2 y = 0. 866 Km + 1. 000 Km = 1. 866 Km, N V 1 x + V 2 x = 0. 500 Km + 1. 732 Km = 2. 232 Km, E
Determine the resultant: 1 st use c^2 = a^2 + b^2 c = (a^2 + b^2)^(1/2) c = [(1. 866 km)^2 + (2. 232 km)^2]^(1/2) So c = 2. 909 km 2 nd use Angle = Inv Tan (Ry / Rx) = Inv Tan (1. 886 km / 2. 232 km) = 39. 9 degrees; The direction is N of E. So R (the resultant) is equal to 2. 909 Km, 39. 9 deg N of E or 2. 909 Km, 50. 1 deg from N, or E of N
