Apply what you've learned about vectors to solve some word problems!

Problem

Amelia flies her airplane through calm skies (no wind) at a velocity (speed and direction) v, start subscript, 1, end subscript, with, vector, on top. The direction of v, start subscript, 1, end subscript, with, vector, on top is 15, degree north of east, and the speed is 180, space, k, m, slash, h.
Eventually, however, she enters a windy part of the atmosphere and finds that her plane now moves at a velocity v, start subscript, 2, end subscript, with, vector, on top. The direction of v, start subscript, 2, end subscript, with, vector, on top is due east, and the speed is 150, space, k, m, slash, h.
(Assume "due east" is 0, degree, "due north" is 90, degree, and so on.)
What is the speed of the wind?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i
space, k, m, slash, h
(Round your final answer to the nearest tenth.)
In what direction is the wind blowing?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i
degree
(Round your final answer to the nearest degree. Your answer should be between 0, degree and 360, degree.)