Question

Two trucks driven by Abby and Brian start at the same position and take off in different directions in an open field. Abby is traveling at a speed of 40 mph in a direction 30° south of west. Brian is traveling at a speed of 56 mph in a direction 75° north of east. What is the speed of Brian's truck according to Abby in mph?

Answer 1

V = 56Mph[75o] - (- 40Mph[210o]) =
Vb = 56[75o] + 40[210]

X = 56*Cos75 + 40*Cos210 = -20.15 Mph
Y = 56*sin75 + 40*sin210 = 34.1 Mph

Vb^2 = (-20.15)^2 + (34.1)^2 = 1568.83
Vb = 39.6 Mph = Brian's speed.