Question

1. how do you combine vectors if they are in opposite directions? a) subtract (or add a negative) b) pythagorean theorem c) use trigonometry d) add 7. how do you determine the horizontal component of a 30 m/s vector at 110 degrees? a) 110 sin 30 b) 30 cos 110 c) 30 sin 110 d) 110 cos 30

Explanation:

Step1: Recall vector - component formula

The horizontal component of a vector $\vec{v}$ with magnitude $v$ and direction $\theta$ (measured from the positive x - axis) is given by $v_x = v\cos\theta$. Here, $v = 30$ m/s and $\theta=110^{\circ}$. So the horizontal component is $30\cos110^{\circ}$.

Step2: Analyze vector combination for opposite - direction vectors

When two vectors are in opposite directions, we subtract (or add a negative). For example, if we have vector $\vec{A}$ and $\vec{B}$ in opposite directions, the resultant vector $\vec{R}=\vec{A}+(-\vec{B})$ or $\vec{R}=\vec{A}-\vec{B}$.

Answer:

6.
a. Subtract (or add a negative)
b. Pythagorean Theorem
c. Use trigonometry
d. Add
7.
a. $110\sin30$
b. $30\cos110$
c. $30\sin110$
d. $110\cos30$
The answer for 6 is a. Subtract (or add a negative) and for 7 is b. $30\cos110$