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Maximum range equation

  1. May 30, 2009 #1
    1. The problem statement, all variables and given/known data
    A projectile is launched 80m/s into the air at angle x to the horizontal off the top edge of an infinitely long hill(inclined plane). The hill makes a 35 degrees angle to the horizontal
    a) Derive an equation for the range(maximum horizontal displacement).
    b) At what angle will the projectile have maximum range?


    2. Relevant equations
    I know the equation for range of an even surface and how to derive it but I don't think that will be of help here.


    3. The attempt at a solution
    Is this question even possible?
    I'm tried to derive an equation but with no luck. That's the hard part. I think I just need to differentiate the equation to get the angle of maximum range.
     
  2. jcsd
  3. May 30, 2009 #2

    LowlyPion

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    Homework Helper

    You can start with the usual equations and the components of the initial velocity in θ.

    The slope adds the additional relationship between the x and y as in

    y/x = tan35
     
  4. May 30, 2009 #3
    U have several way to approach this question.

    1)U may establish the equation representing the way the projectile moving. Establish the equation of the hill. Find the cross point.

    2)(I recommend) U consider the line representing the hill the x axis(picture). Do some math and find the result.

    attachment.php?attachmentid=19150&stc=1&d=1243665976.jpg

    Consider the projectile moves along x and y axis seperately:

    x axis: x=Vo.cosa.t - (sin35.g.t^2)/2 (1)
    y axis: y=Vo.sina.t - (cos35.g.t^2)/2 (2)

    When the projectile touch the hill, y = 0
    So t=0 (starting point) or t= 2.Vo.sina/(cos35.g) (the time it falls)

    Replace t= 2.Vo.sina/(cos35.g) in the equation (1), and u will find the range along the hill (pretty complicated).

    To convert the range along the hill to the horizontal range, just multiply the x with cos35.

    Now u get the result, try to find at which angle the range is max.

    Hard question it is, but do it carefully and u can solve it. Be happy :D
     

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