Question

A worker pushes a wheelbarrow with a force of 20N downward and to the left, as shown in the figure below. The angle the handle makes with the horizontal is 34°. Note that the figure is not drawn to scale. Write the force vector F in the form =F+aibj. Do not round any intermediate computations, and round the values in your answer to the nearest hundredth. f=

Answer 1

The values of F will be "16.58 i + 11.18 j".

Explanation:

The given values are:

Force, F = 20 N

Angle, Ф = 33°

The formula use in the given scenario will be:

⇒
`x=a \ Cos\theta`

⇒
`y=a \ Sin\theta`

Now,

For Force,
`F=ai+bj`

⇒
`a=F \ Cos\theta`

⇒
`=20 \ Cos(34^(\circ))`

⇒
`=20* .829`

⇒
`=16.58`

and,

⇒
`b=F \ Sin\theta`

⇒
`=20 \ Sin(34^(\circ))`

⇒
`=20* .55`

⇒
`=11.18`

So that,

⇒
`F=16.58 \ i+11.18 \ j`