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Velocity vector

  1. Sep 2, 2004 #1
    If [tex]r^{\rightarrow} = bt^2i+ct^3j[/tex], where [tex]b[/tex] and [tex]c[/tex] are positive constants, when does the velocity vector make an angle of [tex]45.0^o[/tex] with the x- and y-axes?


    i & j are vectors.

    i have no clue on how to start it, can anyone give me a hint?
     
  2. jcsd
  3. Sep 2, 2004 #2

    Tide

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    There are several approaches you could take. Here's one:

    A vector that is at right angles to the the 45 degree direction is [itex]\vec a = \hat i - \hat j[/tex]. Now form the scalar product [itex]\vec a \cdot \vec r[/tex] and set it equal to zero. The desired result will follow!
     
  4. Sep 2, 2004 #3

    arildno

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    Alternatively, require that the x and y components of the velocity vector are equal.

    EDIt:
    Tide, I believe he's been given the position vector, not the velocity vector..
     
  5. Sep 2, 2004 #4

    Tide

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    Thanks, arildno! Change that to [itex]\vec a \cdot \vec v[/itex] with [itex]\vec v \frac{d\vec r}{dt}[/itex].
     
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