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I Finding range of a projectile from a graph

  1. Jun 18, 2016 #1
    Hey,
    I am writing a report where I am trying to investigate the effect of initial velocity on the range of a projectile. Does anyone know any graphs I could use to help me find the range?
    Thanks,
     
  2. jcsd
  3. Jun 18, 2016 #2
    upload_2016-6-18_13-26-32.png

    Range of the Projectile fired at an angle θ from the ground with an initial velocity Vi is given by

    upload_2016-6-18_13-26-58.png

    So Range is proportional to square of initial velocity keeping angle of projection θ as constant.

    But I don't understand your question. Which graph you are talking about?
     
  4. Jun 18, 2016 #3
    Apologies, so the report is being done with a sling shot, where the rubberband will be extended to different lengths, as this will affect the initial velocity. Angle is being kept constant and I am not sure which graph to use, however I am expected to manipulate a graph to show the relationship between initial velocity and range, and was wondering if it was possible to find the range through the gradient of a graph.
     
  5. Jun 19, 2016 #4
    What do you mean of the "gradient" of the graph? Your graph must mean the range ##R## versus the initial velocity ##v,## and in this single-variable function, the gradient is just the slope.
     
  6. Jun 19, 2016 #5
    ok yeah I just meant the slope when I said gradient, and was wondering if there were any graphs where the slope is equal to the range, but if not I will just do a graph that shows the range vs initial velocity,
    Thanks,
     
  7. Jun 19, 2016 #6
    If you knew the result ##R=\frac{v^2\sin 2\theta}{g},## then you can easily get the slope ##R'(v)=\frac{2v\sin 2\theta}{g}## and can get what point meets your demand, which, however, the condition seems not meaningful... or?
     
  8. Jun 19, 2016 #7
    ok ye
    ok yeah that makes sense, thanks
     
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