Question

The location of a car at times t1 and t2 is given by the position vectors

r1= 15km due east + 20km due north (time t1) and
r2= 13km due west + 25km due north (time t2)

The units of distance are kilometers

a. What is the magnitude l^rl of the displacement?
b. What angle does the displacement ^r vector make with respect to the x-axis?
c. Draw a graph of the given situation.

Answer 1

a. r1 = (15 + i20)km.
r2 = (-13 + i25)km.

r = r2 - r1\,
r = (-13 + i25) - (15 + i20),
r = -13 + i25 - 15 - i20,
Combine like-terms:
r = -28 + i5,
r = sqrt((-28)^2 + 5^2) =28.4km.

b. r = -28 + i5,
tanA = 5 / -28 = 0.17857,
A = -10.1 deg.,CW.
A = -10.1 + 180 = 169.9 deg.,CCW. Q2.