Question

Two forces are acting on an object, an upward force of 25N and a 45N force to the west. What is the overall magnitude of the force and in what direction?

Answer 1

51.47 Newtons 60.94 to W of N

Step-by-step explanation

Step 1

Free body diagram

Step 2

Magnitude

Let

`\begin{gathered} Vx=-45\text{ N} \\ V_y=25\text{ N} \\ V=\text{ unknonw} \end{gathered}`

so

`\begin{gathered} V=\sqrt[]{V^2_x+V^2_y} \\ \text{replace} \\ V=\sqrt[]{-45^2+25^2} \\ V=\sqrt[]{2650} \\ V=51.47 \end{gathered}`

Step 3

direction

we need to use the tan function

`\begin{gathered} \tan \text{ }\alpha=\frac{opposit\text{e sid}e}{\text{adjacent side}} \\ \text{replace} \\ \tan x=(45)/(25) \\ x=\tan ^(-1)((45)/(25)) \\ x=60.94 \end{gathered}`

therefore,

the answer is

51.47 Newtons 60.94 to W of N