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22 November, 01:15

The world long jump record is 8.95 m (Mike Powell, USA, 1991). Treated as a projectile, what is the maximum range obtainable by a person if he has a take-off speed of 9.5 m/s? State your assumptions.

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  1. 22 November, 01:21
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    The maximum range obtainable by a person if he has a take-off speed of 9.5 m/s is 9.21 m

    Explanation:

    The only assumptions are that

    Acceleration due to gravity = 9.8 m/s²

    The equation for range of a projectile, R = (u² sin 2θ) / g

    u = initial takeoff velocity = 9.5 m/s, θ = angle of jump.

    To attain the maximum range, the (sin 2θ) has to be maximized to 1, that is,

    Sin 2θ = 1 = sin 90°

    2θ = 90°

    θ = 45°

    Therefore, the maximum angle of jump had to be 45°

    R = (9.5² sin (2*45°)) / 9.8 = 9.5²/9.8 = 9.21 m
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