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Homework Help: 2D Motion

  1. Sep 20, 2009 #1
    1. The problem statement, all variables and given/known data

    An object is shot from the origin with a velocity of 50.0 m/s at an angle of 40.0 degrees above the horizontal. What is the range of the object?

    2. Relevant equations
    All the 2D Motion equations - too many to write all out. Ex:

    [tex] V_x = V_0x + a_xt [/tex]

    3. The attempt at a solution
    I don't even think there is enough information given to solve this. I can only solve for
    [tex] V_x [/tex] which is [tex] 50 * cos 40 = 38.3 [/tex] from there I don't know where to go. I try to figure out the y components of this motion, but we don't really know anything about y. We can't really find [tex] V_y [/tex] because to find that we need the equation [tex] V_y = v_0 sin \theta - gt [/tex] but we don't know the time.
  2. jcsd
  3. Sep 20, 2009 #2
    To work out the range we need to work out the flight time. So first find the time it takes the ball to reach it's highest point using the y-component of it's velocity. Then calculate how long it takes to hit the floor. The sum of these two times is the flight time.
  4. Sep 20, 2009 #3
    ARRRGGGHHHHH - silly me. How could I miss that?

    Thank you for pointing me in the right direction, much appreciated m8.
  5. Sep 20, 2009 #4
    Np :)
  6. Sep 20, 2009 #5
    An simpler, more fruitful approach would be to develop two equations, and then turn them into one.

    One would be [tex]x(t)[/tex], the other would be [tex]y(t)[/tex] and combining them will give you [tex]y(x)[/tex]

    That function will describe the height of the object above the the origin as a function of its x-axis distance from the origin. Once you have that function, you can just set [tex]y=0[/tex] to find the x for which this holds true (The range.)

    To get you started, I'll just rewrite your equation:

    [tex]x(t)=v_0\cos{\theta}\cdot t[/tex]


    From here, you should be all set.
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