resolving forces (1 Viewer)

[fgzz]

how do i resolve forces like how would i do i)

 

[liamkk112]

resolve forces really means take the sum of forces (which is equal to ma by newton's 2nd law)
now by drawing a diagram, you can see that:
- there is a force R in the j direction
- there is a force -mgsin(theta) in the i direction
- there is a force -mgcos(theta) in the j direction
so summing the forces you get F = -mgsin(theta)i + (R-mgcos(theta))j
but, the object is not accelerating in the j direction since it is sliding down the slope in the i direction. so the forces balance in the j direction, which gives that
R-mgcos(theta) = 0, and so F = -mgsin(theta)i