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Vector Applications

  1. Feb 9, 2006 #1
    Can anyone explain what to do for these 2 ?

    1.) If a=3i-4j, and b=4i-3j, what is the magnitude of the vector a-b?

    2.) A boy throws a ball at an initial velocity of 26m/s at an angle of 20 degrees above the horizontal. How high above the projection point is the ball after 1.4 seconds ?
  2. jcsd
  3. Feb 9, 2006 #2


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    Staff: Mentor

    For the vector problem, i,j represent usually represent mutually orthogonal (perpendicular) vectors, e.g. in x,y-directions.

    To add two vectors, one adds corresponding components.

    let a = a1i + a2j, and b = b1i + b2j, so a + b = (a1+b1)i + (a2+b2)j. The subtraction is just the additive inverse, i.e. replace + with -.

    The magnitude of a is just sqrt(a12+a22). Remember the formula for the length of the hypotenuse of a right triangle - Pythagorean theorem.

    In question 2, one has to resolve the vector given by "26m/s at an angle of 20 degrees" into horizontal and vertical components. The ball travels vertically with some velocity component, but decelerates due to gravity, reaches a maximum at some time T, and returns to the same initial elevation at time 2T (i.e. T up and T down - neglecting air resistance).

    Using the vertical velocity component, one can establish the equation of motion as a function of time to determine where the ball is at 1.4 s. If T (time to max height) < 1.4 s, then the ball is falling back from its maximum altitude.
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