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Vector word problems

Anjali's plane had been flying through calm skies (no wind) with a velocity (speed and direction) vector v1=(400,100)\vec{v_1} = (400,100). Now, however, the air mass surrounding the plane is moving quickly (i.e.i.e., it's windy). Although Anjali has not adjusted any of the controls in the cockpit, the plane's new velocity is v2=(350,50)\vec{v_2} = (350, 50).
(Speeds are in kilometers per hour.)
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}
kilometer per hour
(Round your final answer to the nearest tenth.)
In what direction is the wind blowing? Assume 00 is the rightward direction.
  • 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}
radians
(Round your final answer to two decimal places. Your answer should be between 00 and 2π2\pi.)