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Finding Initial Speed Given Range

  1. Sep 14, 2014 #1
    1. The problem statement, all variables and given/known data
    If you want to use a catapult to throw rocks, and the max range is 0.67 km, what initial speed must the rocks have as they leave the catapult?


    2. Relevant equations

    v=Δr/Δt




    3. The attempt at a solution
    I sketched a graph of the projectile trajectory with the desired range on the x-axis. I also converted 0.67 km to 670 m. I concluded that acceleration would be -9.8 m/s. I couldn't go any further since I feel like I am not given enough information to work with.
     
  2. jcsd
  3. Sep 14, 2014 #2

    Simon Bridge

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    ... you need to know the angle the stones are launched at - you are told this though. The way the question is written suggests you have already derived or had given to you a bunch of equations for range, max-height and so on. If not, then try sketching velocity-time graphs for the horizontal and vertical components of the motion.

    note: the acceleration is -9.8m/s/s in the +y direction, taking +y to be "upwards".
     
  4. Sep 14, 2014 #3
    Thank you for the quick response. I used the formula Rmax=V02/g. After substituting the givens into the formula, I came up with 81 m/s
     
  5. Sep 16, 2014 #4

    Simon Bridge

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    Did you understand where the equation came from?
     
  6. Sep 16, 2014 #5
    Not quite, although a similar formula that I know is R=(V0^2)sin(2t)/g
     
  7. Sep 16, 2014 #6
    I also understand that for the range to be max, the angle has to be 45, and if we put 45 into the V0^2sin(2t)/g formula, sin2t would just be 1, and we are left with just V0^2/g
     
  8. Sep 16, 2014 #7

    Simon Bridge

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    ... well done :)

    I just don't like the style of teaching that has students memorize a bunch of equations.
    Note: that equation only works where the initial and final heights are the same - when you can derive the equations from velocity-time graphs you'll be able to do any ballistics problem, and many more besides, without having to memorize or look up any equations ... so it's a skill worth obtaining.
     
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