Question

The magnitude and direction exerted by two tugboats towing a ship are 1610 kilograms, N30°W, and 1250 kilograms, S55°W, respectively. Find the magnitude, in kilograms, and the direction angle, in degrees, of the resultant force.Question content area bottomPart 1The magnitude of the resultant force is enter your response here kilograms.

Answer 1

let's start by drawing a diagram of the situation

In order to find the magnitud of the resulting force we need to find the forces towards the west direction

Then

`\begin{gathered} F_x=F_(1x)+F_(2x) \\ \end{gathered}`
`\begin{gathered} F_(1x)=1610\cdot\sin 30=1610\cdot(1)/(2)=805 \\ \end{gathered}`
`F_(2x)=1250\cdot\sin 55=1023.94`

Thus,

`F_x=805+1023.94=1828.94`

In the y axis we have:

`\begin{gathered} F_y=F_(1y)+F_(2y) \\ F_y=1610\cos 30+1250\cos 55 \\ F_y=1394.30+716.97 \\ F_y=2111.27 \end{gathered}`

Then, finally, we add both forces as follows

`F=\sqrt[]{(F_x)^2+(F_y)^2_{}}_{}`

replacing

`\begin{gathered} F=\sqrt[]{1828.94^2+2111.27^2} \\ F=2793.29 \end{gathered}`

Then the magnitud of the resulting forces in x and y directions is: 2793.29 kg