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Range of a Ballista Arrow

  1. Sep 25, 2012 #1
    1. The problem statement, all variables and given/known data
    A ballista fires an arrow at an initial velocity of 325 m/s. What is the maximum range it can reach? How high would it get at maximum range? How long would it take?


    2. Relevant equations
    Rmax = (Vo^2)/g


    3. The attempt at a solution
    When I used the formula, I got the maximum range to be 10,778 m. This is close to 6 miles, which is obviously unrealistic. What's wrong here?
     
  2. jcsd
  3. Sep 25, 2012 #2
    1170km/h.
    Very powerful ballista.
     
    Last edited: Sep 25, 2012
  4. Sep 25, 2012 #3
    It's in my text book. But the range equation it R = (Vo^2/g)*sin(2Ɵ). Since firing at an angle of 45 degrees yields maximum range, when theta becomes 45, sin(2Ɵ) is equal to 1 and can be taken out of the formula.
     
  5. Sep 25, 2012 #4
    What do you mean by this? That's a velocity, not a distance.
     
  6. Sep 25, 2012 #5
    The initial speed given is just above the speed of sound at sea level. Which is completely not realistic for a ballista. But even if it were, the range equation you use would also be unrealistic, because it neglects air resistance. Which cannot be neglected at supersonic speeds.
     
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