Question

#4 on this review and I think I’m going in the right direction so far

Answer 1

Given: Force 12N and 14N

To Determine: The strength and the direction of the resultant

Solution

The strength of the given is the magnitude of the resultant

The result is R in the diagram above

Using Pythagoras theorem

`\begin{gathered} R^2=12^2+14^2 \\ R^2=144+196 \\ R^2=340 \\ R=√(340) \\ R=2√(85)N \\ R=18.439N \end{gathered}`

From the diagram

`\begin{gathered} tan\theta=(12)/(14) \\ tan\theta=(6)/(7) \\ \theta=tan^(-1)((6)/(7)) \\ \theta=40.6^0 \end{gathered}`

The direction of the resultant is

`Direction-of-the-resultant=90^0+40.6^0=130.6^0`

Hence:

The strength of the resultant is 18.4N

The direction of the resultant is 130.6⁰