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An outfielder throws a baseball with an initial speed of 30 m/s at an angle of 13° to the horizontal. The ball leaves his hand from a height of 1.75 m. How long is the ball in the air before it hits the ground?

  • physics -

    Upward motion:
    v(y) = v(oy)- g•t1.
    At the highest point v(y) = 0,
    t1 =v(oy)/g = v(o) •sinα/g =
    =30•sin 13º/9.8 = 0.69 s.
    hₒ = v(oy) •t1- g•t1²/2= v(o)•sinα•t1 - g•t1²/2=
    =30•sin 13º•0.69 – 9.8•(0.69)²/2 = 4.66-2.33 =2.33 m.
    H = h + hₒ =1.75 +2.33 = 4.08 m.
    v(x) = v(ox) = v(o) •cosα = 30•cos13º = 29.23 m/s.
    Downward motion:
    The time of downward motion is determined by the time of vertical motion from the height H:
    H=g•t2²/2,
    t2 =sqrt(2•H/g) =
    =sqrt(2•4.08/9.8) =0.91 s.
    t =t1+t2 = 0.69 +0.91 = 1.6 s.

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