A hiker leaves camp hikes 6 miles 18degree North of East the

A hiker leaves camp, hikes 6 miles 18degree North of East, then turns and hikes 5 miles 34degree South of East, finally turns again and hikes 4 miles 22degree West of South. Assume each displacement is in a straight line. Refer to the diagram and use vector addition to find the net displacement, and then express the answer as a total distance and direction from camp at the initial location. Show your work.

Solution

D1 = 6 <30 deg

D2 = 5<34deg

D3 = 4 <22deg

net diplacement : D = D1 +D2 +D3

X axis Dx = 6cos30 + 5cos34 - 4sin22 = 7.843 mi

Y axis Dy = 6sin30 -5sin34 - 4cos22

= -3.504 mi

Net Diplacement = D = sqrt(Dx^2 +Dy^2)

= sqrt( 7.843^2 +3.504^2) = 8.59 mi

Angle = tan^-1(Dy/Dx) = tan^-1(-3.504/7.843) = 24.07 deg from vertical y axis inIVrth quadrant