Question

Find the magnitude of the resultant (sum) of their two forces. What is the angle the resultant forms with Brianna's force?

Andre and Brianna are both pulling on a crate with ropes. Andre pulls with an 18 N force, and Brianna pulls with a 23 N force, as shown in the diagram.

Answer 1

Resultant vector `vecC` of two vectors as shown in the figure is given by the expression

`|vecC|=sqrt(|vecB|^2+|vecA|^2+2|vecB||vecA|cos theta)`

Inserting given values we get

`|vecC|=sqrt(23^2+18^2+2xx23xx18xxcos51^@`
`|vecC|=37.07N`, rounded to two decimal places.

Direction of the vector `alpha` is given by

`alpha=tan^-1((|vecA|sintheta)/(|vecB|+|vecA|costheta))`

Inserting given values we get

`alpha=tan^-1((18sin51^@)/(23+18cos51^@))`
`alpha=tan^-1(0.4075)`
`alpha=22.2^@` rounded to one decimal place.