Question

Logan pushes a box with a 400n of force with a direction angle of 30 degrees, while Andrew pushes the same box with a force of 250N with a direction angle of 290 degrees.Which of the following represents the component vectors of the force applied by Andrew?

Answer 1

Given:

The force applied by the logan is

`F=400\text{ N}`

The force applied by the Andrew is

`F=250\text{ N}`

Required: component of force applied by the andrew.

Step-by-step explanation:

first, draw the free body diagram,

from the free body diagram we can write resolve the force into two components

one along the y axis and one along the x axis

Along x axis

`F\sin(290^(\circ))`

Plugging the values, we get

`\begin{gathered} =250*\sin(290) \\ =250*-0.939 \\ =-234.92\text{ N} \end{gathered}`

Along y axis

`\begin{gathered} F\cos(290^(\circ)) \\ =250*\cos(290^(\circ)) \\ =250*0.342 \\ =85.50\text{ N} \end{gathered}`

Thus, the component of forces are

`85.50\text{ N, }-234.92\text{ N}`

and option first is correct.