A man is pulling on his dog with a force of 70.0 N directed at an angle of +30.0° to the horizontal. What are the x and y components of this force?
To put it shortly, any force F making an angle
He is pulling his dog at an angle of 30 with the horizontal with a force of 70 N
There are an x component and a y component to this force
If we draw this as a vector, then the diagram looks something like this
The Black line is the direction of force and red and green are x and y components respectively. The angle between the Black line and Red line is 30 degrees as given
Since force is a vector, we can move the arrows and rewrite it as
Now since the angle between the Black line and the Red line is 30 degrees and the vector black line has a magnitude of 70 N, we can use trigonometry
The x component is
So the components are
y-direction= 35.0 N
x-direction= 60.6 N
You essentially have a right-angled triangle with a 30-degree angle and a hypotenuse with a magnitude 70.0 Newtons.
So the vertical component (y-direction) is given by=
The horizontal component (x-direction) is given by