Question

I need to find part e n fOur A vector =(30m)x+(-8.0)yB=(4.5m)x+(18m)y

Answer 1

ANSWERS

E. Direction = 16°

F. Magnitude = 36 m

Step-by-step explanation

Given the vectors:

`\begin{gathered} \vec{A}=(30m)\hat{x}+(-8.0m)\hat{y} \\ \vec{B}=(4.5m)\hat{x}+(18m)\hat{y} \end{gathered}`

We have to find the vector that results from adding these two vectors. To do so, we have to add the components,

`\begin{gathered} \vec{A}+\vec{B}=(30m+4.5m)\hat{x}+(-8.0m+18m)\hat{y} \\ \vec{A}+\vec{B}=(34.5m)\hat{x}+(10m)\hat{y} \end{gathered}`

Now we have to find the direction and magnitude of the vector.

E. The direction is,

`\theta_{\vec{A}+\vec{B}}=\tan ^(-1)((y)/(x))=\tan ^(-1)((10)/(34.5))\approx16\degree`

F. The magnitude is the square root of the sum of the squares of the components,

`\vecA+\vec{B}|=\sqrt[]{34.5^2+10^2}=\sqrt[]{1290.25}\approx36m`

Hence the direction of the sum of vectors A and B is 16° (rounded to the nearest degree) and the magnitude of the resultant is 36 meters (rounded to the nearest meter)