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Projectile motion and acceleration HELP!

  1. Sep 12, 2009 #1

    nrw

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    1. The problem statement, all variables and given/known data

    A lemming accelerates uniformly starting from rest 2 meters before jumping horizontally from the top of a 20 m high cliff. What is the minimum acceleration required so that the lemming can clear the rocks stretching out 4 m from the base of the cliff?

    2. Relevant equations
    I know that we have both an X and Y component we need to calculate, but what is confusing to me is that - how does the 2 meters at the beginning play into the horizontal velocity? And since the lemming is jumping horizontally - what does that mean? Does that mean something other than free fall? Is the initial velocity of the jump the final velocity of the horizontal velocity?

    3. The attempt at a solution
    I have tried this several ways, but have no idea if I'm doing it right. For the X component, I have the initial velocity is 0, the final velocity is unknown, the displacement is 2 m (??) and acceleration is 0 (because can acceleration exist in a horizontal dimension?) and the t is unknown. For the y component, I have the initial velocity as 0, but I don't know if this is correct? The acceleration is -10 m/s2, the Y displacement is -40. So, do I use the pythagorean theorem to find the final velocity of Y? I'm totally confused about where to start. Thanks!!!!!
     
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  3. Sep 12, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi nrw! Welcome to PF! :smile:

    Let's restate the problem more clearly …

    i] a projectile leaves the top of a 20m cliff, with initial velocity purely horizontal, and lands 4m from the base: what is its initial speed, v0?

    ii] what acceleration must it have had to get from rest to v0 after 2m?
     
  4. Sep 12, 2009 #3

    nrw

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    Thanks! So when the initial velocity is purely horizontal, that means that we are assuming the initial speed of the fall is 0 and thus, the y-component is calculated using simple free fall acceleration?
    I first calculated the time it would take the lemming to land if it were free falling... using y=Vi (t) - 1/2 a t2. This gives me 2 seconds. Then, if the lemming has only 2 seconds to clear 4 m, it must have a velocity of 2 m/s2 (using x=vt). Then, to calculate the acceleration, I use v2 = vi2 + 2aX and get the acceleration of 1 m/s.
    Does that sound right?
    I guess I'm confused about when to use a = -9.8 (all falls?) and when to break a equation up into both X and Y components.
    Thanks!!!
     
  5. Sep 13, 2009 #4

    tiny-tim

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    Yup! :biggrin:
    Using g = 10, yes. :smile:
    Don't ask yourself "what is the acceleration?" …

    ask yourself "what is the force?"

    If it's gravity, then it's 9.8 (or 10 :wink:) …

    if it's an applied force, then it isn't 9.8 !

    (of course, sometimes it's both … eg a rocket)

    But you must always break it up into X and Y components (or surface and normal, or whatever) …

    F = ma is a vector equation, and you must treat it as such (unless of course the motion is obviously one-dimensional, in which case one of the component equations will be 0 = 0 :wink:)
     
  6. Sep 13, 2009 #5

    nrw

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    Wow! Thank you so much for your help! Thinking of acceleration as force really helps - I appreciate your time and the way you ex;lain things!
     
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