A) Vector A
The x-component of a vector can be found by using the formula
[tex]v_x = v cos \theta[/tex]
where
v is the magnitude of the vector
[tex]\theta[/tex] is the angle between the x-axis and the direction of the vector
- Vector A has a magnitude of 50 units along the positive x-direction, so [tex]\theta_A = 0^{\circ}[/tex]. So its x-component is
[tex]A_x = A cos \theta_A = (50) cos 0^{\circ}=50[/tex]
- Vector B has a magnitude of 120 units and the direction is [tex]\theta_B = -70^{\circ}[/tex] (negative since it is below the x-axis), so the x-component is
[tex]B_x = B cos \theta_B = (120) cos (-70^{\circ})=41[/tex]
So, vector A has the greater x component.
B) Vector B
Instead, the y-component of a vector can be found by using the formula
[tex]v_y = v sin \theta[/tex]
Here we have
- Vector B has a magnitude of 50 units along the positive x-direction, so [tex]\theta_A = 0^{\circ}[/tex]. So its y-component is
[tex]A_y = A sin \theta_A = (50) sin 0^{\circ}=0[/tex]
- Vector B has a magnitude of 120 units and the direction is [tex]\theta_B = -70^{\circ}[/tex], so the y-component is
[tex]B_y = B sin \theta_B = (120) sin (-70^{\circ})=-112.7[/tex]
where the negative sign means the direction is along negative y:
So, vector B has the greater y component.
