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March 25, 2017

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A soccer ball is kicked from the ground with an initial speed of 14.5 m/s. After 0.272 seconds, ts speed is 12.4 m/s. (A) Give a strategy that will allow you to calculate the ball's initial direction of motion. (B) Use your strategy to find the initial direction.

  • physics - ,

    v₀⒳= v₀•cosα,
    v₀⒴ =v₀•sinα,
    v₀² =v₀⒳² +v₀⒴²,
    v² =v⒳² +v⒴²,
    v⒳= v₀⒳,
    v⒴=v₀⒴ -g•t,
    v² =v⒳² +v⒴² = v₀⒳²+(v₀⒴ -g•t)²=
    =v₀⒳²+v₀⒴² -2 v₀⒴•g•t +(g•t)² =
    = v₀²-2 v₀•sinα•g•t +(g•t)².
    sinα= [v₀²-v²+(g•t)²]/2•v₀•g•t =
    =[14.5² -12.4²+(9.8•0.272²]/(2•14.5•9.8•0.272) =
    =0.823.
    α=55.35°

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