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Solving A problem using kinematics and Energy

  1. May 13, 2015 #1
    1. The problem statement, all variables and given/known data
    A ##1.50## kg snowball is fired from a cliff ##12.5##m high with an initial velocity of ##14.0## m/s, directed ##41^{\circ}## above the horizontal. How fast does the ball travel when it hits the ground.

    2. Relevant equations
    ##E=K+U##
    ##V^2_f=v^2_i+2a(y_f-y_i)##
    ##y_f=v_i \sin \theta-gt^2##


    3. The attempt at a solution
    First using conservation of mechanical energy,
    ##E=(1/2mv_f^2-1/2mv^2_i)+(0-mgh)##
    ##v=\sqrt{v^2_i+2mgh} \implies v=\sqrt{14^2+2((9.8)(12.5)}=21m/s##

    Using kinematics to verify,
    ##0=v_i\sin \theta -gt##
    ##t=\frac{v_i\sin \theta}{g}=\frac{14\sin 41}{9.8}=0.937 s##
    ##y_f=14\sin 41 (.937)-.5(9.8)(.937)^2=4.3m## which gives the height traveled above the horizontal
    Calculate speed ##v=\sqrt{2(9.8)(12.5+4.3)}=18.14m/s##

    Which is wrong they both look correct.
     
  2. jcsd
  3. May 13, 2015 #2

    SammyS

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    The first method looks correct.

    In the second method, you completely ignored the horizontal component of the velocity.
     
  4. May 13, 2015 #3
    How is the horizontal component needed? The only thing we are concerned with is the height, thus once the snowball reaches maximum height, it becomes a one dimensional problem regardless of how fast the horizontal component is traveling. It is independent of gravity.
     
  5. May 13, 2015 #4

    SammyS

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    How is it not needed?

    Aren't you asked:
    How is speed related to velocity?
     
  6. May 13, 2015 #5
    So you need to calculate ##v_f=\sqrt{v_x^2+v_y^2}=\sqrt{14^2\cos^2 41^{\circ}+(18.14)^2}=20.99## I guess that what was missing thanks.
     
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