What is the direction of their vector sum?

Question

Vector G is 40.3 m long in a -35.0 degree direction. Vector H is 63.3 m long in a 270 degree direction. What is the direction of their vector sum?

Answer 1

The easiest way to tackle this problem is by breaking the vectors up into their components (also it's easier to type this method).

G = 40.3 cos (-35.0°) i + 40.3 sin (-35.0°) j ----where i denotes the x direction and j denotes the y direction

H = 63.3 sin (270°) j ----- I left off the i component because i know cos 270 is 0.

40.3 and 63.3 are the magnitudes of your vector, or the hypotenuse of a triangle. We are finding the horizontal (Adjacent) and vertical (Opposite) legs the respective hypotenuse (we have to remember SOH COH TOA)

Now you can simply add components

G + H = (40.3 cos (-35.0)) i + (40.3 sin (-35.0°)+ 63.3 sin (270)) j ----be sure to pay close attention to signs when doing your calculations on your calculator.

Answer 2

Vector G is 40.3 m long in a -35.0 degree direction. Vector H is 63.3 m long in a 270 degree direction. What is the direction of their vector sum?

Vector G x-component = 40.3•cos(-35°) = 33.01m

y-component = 40.3•sin(-35°) = -23.12m

Vector H x-component = 63.3•cos(270°) = 0

y-component = 6.3•sin(270°) = -63.3m

To get R_x, add G_x and H_x = 33.01+0 = 33.01m

To get R_y, add G_y and H_y = (-23.12)-63.3 = -86.42m

Direction is the angle from the positive x-direction.

angle θ = tan^-1(Ry/Rx) = -69.1°

R = √(R_x² + R_y²) = √(33.01² + (-86.42²)) = 92.5m

If you need further clarification or if you are looking for 1-on-1 tutoring, let me know.

Mr. A (Frank)