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Relative Velocity - Mistake in Textbook?

  1. Jul 26, 2013 #1
    I am just reading through this free online textbook and it seems to me that there is a mistake on page 24.

    http://www.anselm.edu/internet/physics/cbphysics/downloadsI/cbPhysicsIa18.pdf#page=23

    He describes the muzzle velocity, which he defines as the relative velocity between two objects, as being the sum of the two objects. Which in this case is:

    vM=vB+vC

    This is not the relative velocity, this would be the relative velocity between these two objects:

    vM=vB-vC

    Am I missing something really simple or is this actually a mistake?
     
  2. jcsd
  3. Jul 26, 2013 #2

    HallsofIvy

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    You would be correct if [itex]v_B[/itex] and [itex]v_C[/itex] were "vectors" or (in one dimension) "signed quantities" so that with the cannon ball going to the right, [itex]v_B[/itex] were positive and with the cannon rolling to the left, [itex]v_C[/itex] would be negative. But here they are clearly using the speeds or "unsigned quantities", not velocities.

    For example, if the cannon ball went to the right at, say, 300 m/s while the cannon rolled back at 2 m/s. then, as velocities or "signed quantities" we would say that [itex]v_B= 300[/itex] and [itex]v_C= -2[/itex] so that the "relative velocity" would be [itex]v_B- v_C= 300- (-2)= 302[/itex] m/s. But the book is using the "unsigned" speeds: [itex]v_B= 300[/itex] m/s to the right and [itex]v_C= 2[/itex] to the left so that the relative speed is [itex]v_B+ v_C= 300+ 2= 302[/itex] m/s to the right.
     
  4. Jul 26, 2013 #3
    Yes, this would make sense. I guess their use of the word velocity threw me off.
     
  5. Jul 26, 2013 #4

    Redbelly98

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    That's understandable. Reading it carefully, I noticed they make statements along the lines of "the velocity is vB to the right". Since they specify a direction, they are correct to use "velocity" rather than "speed". However, vB by itself (with no direction specified) is a speed, not a velocity.
     
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