Question

13. (5 pts) Find the resultant of 33 m at 74o and 52 m at -35o.

A) Calculate the sum of the displacements in the x-direction. Keep six sf.

B) Calculate the sum of the displacements in the x-direction. Keep six sf.

C) What is the magnitude of the resultant of the displacement? Keep two sf.

D) What is the angle of the resultant in degrees? Keep two sf.

(SF means significant figures)

Answer 1

33 m at 74 deg

52 m at -35 deg

(A) Sum of displacement in the x - direction -

X = [33*cos74 + 52*cos(-35)] m = [9.09603 + 42.59591] m = 51.6919 m (Answer)

(B) Sum of displacement in the y - direction -

Y = [33*sin74 + 52*sin(-35)] m = [31.7216 - 29.8260] m = 1.89560 m (Answer)

(C) Magnitude of the resultant displacement = sqrt [X^2 + Y^2] = sqrt[51.6919^2 + 1.89560^2] = 52.0 m (Answer)

(D) Angle of the resultant, = tan^-1(Y/X) = tan^-1(51.6919/1.89560) = 88.0 deg. (Answer)