Question

A truck driver travels a distance of 100 miles due East. He then turns at an angle of 35 degrees S of E and travels a distance of 50 miles.

What is the resultant displacement?
What is the direction?

Answer 1

Just add the two vectors.

The eastward displacement is
X = 100 + 50 cos35 = 140.96 miles

The northern displacement (assuming north is positive) is
Y = -50 sin35 = -28.68 miles
(The minus sign is there because the second vector is south of east, not north).


Total displacementis
= sqrt[(140.96)^2 + (-28.68)^2]

The direction(measured south of east) is tan^-1 (28.68/140.96) = 11.5 degrees