A crate is dragged across a horizontal floor by applying a force of magnitude 30N. The force makes an angle of 40∘ above the horizontal. The crate undergoes a displacement given by s=6i^+2j^m where i^ is horizontal and j^ is vertically upward.
Solve the following:
a. (i) Calculate the scalar projection of the force on the displacement.
b. (ii) Hence, determine the work done by the force during the displacement.
c. (iii) Obtain the magnitude and unit-vector form of that component of the force which is perpendicular to the displacement.