A box sits on a plane that is tilted 25° above the horizontal. A horizontal force of 30N acts on the box. Use trigonometry to write the force in vector component form using (a) a standard coordinate system, and (b) a coordinate system tilted to align itself with the plane.

F (x) = 30i N

F = 27.2 i + 12.7 j

Explanation:

Given data

angle = 25°

horizontal force = 30N

to find out

force standard coordinate system and align itself with the plane

solution

in 1st part

we know according to question force acts on the box is horizontal is 30N

so force in vector is F (x) = 30i N

and

in 2nd part

we know plane is tilted at 25° above horizontal.

so F (x) = 30 cos 25°

and F (y) = 30 sin 25°

F (x) = 27.2 N

F (y) = 30 sin 25°12.7 N

so total F = F (x) + F (y)

F = 27.2 i + 12.7 j