Question

How is this solved, I have been pulling my hair for hours

Answer 1

Option (C)

Step-by-step explanation:

We are given the magnitude and direction of two vectors, a and b. The questions asks us to find the x-component of their vector sum.

`\vec a =12 \ m \ at \ 40 \textdegree\\\\\vec b =9 \ m \ at \ 160 \textdegree\\\\\\\hrule`

Finding the x-component of each vector using the given information.

Finding a_x:

`a_x=\vec a\cos(\theta)\\\\\\\\\Longrightarrow a_x=(12)\cos(40 \textdegree)\\\\\\\\\therefore a_x \approx 9.19253`

Finding b_x:

`b_x=\vec a\cos(\theta)\\\\\\\\\Longrightarrow b_x=(9)\cos(160 \textdegree)\\\\\\\\\therefore b_x \approx -8.45723`

Find the vector sum by adding a_x and b_x together.

`\therefore \boxed{\boxed{a_x+b_x \approx 0.7353}}`

Thus, option (C) is correct.