a.

Since the blue dot represents the child as the origin, the rectangular components for a force will

be the horizontal and vertical components of the force.

Observe the diagram :

The force of friction is applying of force to the left parallel to the -axis and

of  force up parallel to the -axis.

Therefore, force .

Normal force is applying of force to the right parallel to the -axis and of

force up parallel to the -axis.

Therefore, normal force .

Weight is applying  of force down parallel to the y-axis.

Therefore, weight is .

b.

To find the component form of the resultant vector representing the force that causes the child to

move down the slide, add three force vectors, .

The component form of the resultant vector representing the force is .

a.

Force .

Normal force .

Weight .

b.

The component form of the resultant vector representing the force is .