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

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.)