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Maximum height of projectile motion

  1. Oct 3, 2004 #1
    I'm having major problems figuring this one out.

    The question is from the book, yet their are no sample problems and a handful of given formulas. I've played around with the formulas with substitution, etc and I've end up with the wrong answer.

    Given: Angle of projectile fired and final displacement along X axis.

    angle = 25 degrees
    final displacement of x = 301.5 m
    accleration = -9.81m/s^2


    Find: Maximum height of Y.

    any ideas how I can manipulate the standard formulas of projectile motion to solve for this problem?
     
  2. jcsd
  3. Oct 3, 2004 #2

    Chi Meson

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    horizontal displacement = v(cos theta) t
    vertical displacement = 0 = v(sin theta)t + 1/2 (-9.8) t^2

    re-arrange each formula, solving for t, and set them equal to each other.
    THen solve for v
    then solve for max height.
     
  4. Oct 3, 2004 #3
    You could also use the range equation to solve for initial velocity. Then use that to find max height.
     
  5. Oct 3, 2004 #4
    can you help me find my mistake. i worked it out to the best of my ability.

    rearranging displacement of x
    t = 301.5m / v cos 25

    rearranging displacement of y
    t = -2 ( v sin25) / -9.81

    than using t = t

    -2 ( v sin 25) ( v cos 25) = 301.5 (-9.81) -->

    V^2 = sqroot [ (301.5(-9.81)) / -2 sin25 cos 25

    V = 62.1 m/s

    T = 301.5m / 62.1m/s cos 25 = 5.36s

    maximum height with no air resistance would be at half of time
    displacement of y = v sin 25 ( t ) + (1/2) (-9.81) (t^2)

    y = 62.1 sin 25 (2.68) + 1/2 (-9.81) (2.68^2)

    maximum y = 70.3 - 35.2 = 35.1

    answer in book says it is 70.3m

    what did i do wrong?
     
  6. Oct 4, 2004 #5
    maybe this will help

    Exact question from book: A golfer can hit a golf ball a horizontal distance of over 300 m on a good drive. What maximum height will a 301.5m drive reach if it is launched at an angle of 25.0 degrees to the ground? (Hint: At the top of its flight, the ball's vertical velocity component will be zero)
     
  7. Oct 4, 2004 #6
    Your calculations are correct!

    -- AI
     
  8. Sep 29, 2011 #7


    I found this video helpful! check it out
     
    Last edited by a moderator: Sep 25, 2014
  9. Sep 29, 2011 #8


    I found this video helpful! check it out
     
    Last edited by a moderator: Sep 25, 2014
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