Question

A hiker starts at his camp and moves the following distances while exploring his surroundings: 67.0 m north, 2.00 ✕ 10² m east, 1.00 ✕ 10² m at an angle 30.0° north of east, and1.50 ✕ 10² m south.a) Find his resultant displacement from camp. (Take east as the positive x-direction and north as the positive y-direction.)

Find his resultant displacement from camp. (Take east as the positive x-direction and north as the positive y-direction.)

mangnitude

direction east of south

Answer 1

The components of the resultant displacement are

Rx = Ax + Bx + Cx +Dx = 0+ 250 m +100 m cos 30 + 0 = 336.6 m

Ry = Ay + By + Cy + Dy = 67 +0+ 100 sin 30 - 150 = -33 m

resulatant displacemnt is

R = root Rx^2 + Ry^2 = root (336.6 m)^2+ ( -33 m)^2 = 338.21 m

direction is

theta = tan^-1 ( -33/ 336.6 ) = -5.59

-5.59 east of south