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

Mighty Casey hits two baseballs out of the park. The path of the first baseball can be described by the displacement (distance and direction) vector b1=100i^+10j^\purple{\vec{b_1}} = 100 \hat i + 10\hat j. The path of the second baseball can be described by the displacement vector b2=90i^+(20)j^\blue{\vec{b_2}} = 90\hat i + (-20)\hat j.
(Values above are given in meters.)
How much farther did the first ball travel than the second?
  • 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
meters
(Round your final answer to the nearest tenth.)
How far are the baseballs apart?
  • 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
meters
(Round your final answer to the nearest tenth.)