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How to find the muzzle velocity of a launcher?

  1. Sep 28, 2014 #1
    I'm currently working a lab that requires me to find the muzzle velocity (initial velocity) of my launcher. The only information I have is the launch angle, horizontal distance, maximum height and time. Is there a specific equation that I have to use? Should I be using trig equations with projectile motion equations?
  2. jcsd
  3. Sep 28, 2014 #2
  4. Sep 28, 2014 #3
    Alright but which ones?
  5. Sep 28, 2014 #4


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    You need to choose a motion equation that contains initial velocity and doesn't contain any variables whose values are not specified in the problem.

    Alternatively, use conservation of energy.
  6. Sep 28, 2014 #5
    Okay say the launch angle is at 90 degrees, max.height is 110cm, horizontal range is 525cm, time is 2.4s, what equation would i use to solve for initial velocity?
  7. Sep 28, 2014 #6


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    Are you familiar with parabolic motion? If so you should be able to derive a relationship between some of the quantities that you have.

    These values are inconsistent. If you fire straight up into the air, how is the projectile going to get a horizontal velocity component?
  8. Sep 28, 2014 #7
    Opps I meant 45 degree sorry about that but thank you
  9. Sep 28, 2014 #8


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    What kinematic equations do you know? Which one do YOU think you should use?
    Perhaps you know how to write down a conservation of energy equation instead?

    This is a homework-type question, and we are not supposed to give you a straight answer. You need to show some work.
  10. Sep 28, 2014 #9


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    Still inconsistent.
    Actually, if you have so many known quantities, you have multiple independent ways to calculate those values and you can check if they agree with each other.
  11. Sep 28, 2014 #10
    Even after setting the launch angle at 45 degrees, the values are still inconsistent. If the projectile is in the air for 2.4 seconds, it takes 1.2 seconds to rise to the top, when the vertical velocity is 0. Since the acceleration of gravity is 9.8 m/s, and you have v_vert(t) = v_vert_0 - gt, you have at 1.2 seconds: v = 0 = v_vert_0 - g(1.2) = 0, so v_vert_0 = 1.2g = 11.8 m/s. That will produce a height much bigger than 1.1 m.

    Even if you ignore the value for t, you can compute the launch speed from :
    - the launch angle and the maximum altitude.
    - the launch angle and the horizontal range.
    These are both pretty simple, but you get values for v that differ by 12%
  12. Sep 29, 2014 #11
    The inconsistency disappears if you don't assume the projectile lands at the same altitude it was launched from. e.g. It could be launched from a table and land on the floor.

    O.P. Does the context of the problem allow for that possibility?
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