Learn To Be brings free online tutoring students around the United States. Volunteer and gain community service hours while helping students who need it./p>

Vector word problems

Amelia flies her airplane through calm skies (no wind) at a velocity (speed and direction) v1\vec{v_1}. The direction of v1\vec{v_1} is 1515^\circ north of east, and the speed is 180km/h180\,\text{km/h}.
Eventually, however, she enters a windy part of the atmosphere and finds that her plane now moves at a velocity v2\vec{v_2}. The direction of v2\vec{v_2} is due east, and the speed is 150km/h150\,\text{km/h}.
(Assume "due east" is 00^\circ, "due north" is 9090^\circ, and so on.)
What is the speed of the wind?
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
km/h\,\text{km}/\text{h}
(Round your final answer to the nearest tenth.)
In what direction is the wind blowing?
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
^\circ
(Round your final answer to the nearest degree. Your answer should be between 00^\circ and 360360^\circ.)