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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.


    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:


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


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


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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


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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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