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An athlete executing a long jump leaves the ground at a 32.5° angle and travels 7.72 m. What was the take-off speed?

If this speed were increased by just 4.9 %, how much longer would the jump be?

  • Physics -

    The formula you need to answer both questions is

    Distance = Vo^2*sin(2A)/g

    where A it the takeoff angle.

    Deriving that formula would be a good exercise for you. You would use the trig identity sin(2A) = 2 sinA cosA.

    In the first case,
    Vo^2 = g*7.72m/sin65 = 83.56 m^2/s^2
    Take the square root of that for Vo.

    Increasing the speed by a factor 1.049 will increase the length of the jump by a factor (1.049)^2 = 1.100
    (a 10.0% increase).

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