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24 April, 03:50

In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole. Find the minimum speed must the athlete leave the ground in order to lift his center of mass 1.65 m and cross the bar with a speed of 0.75 m/s.

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  1. 24 April, 06:00
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    The answer to your question is v₁ = 5.74 m/s

    Explanation:

    Data

    v₁ = ?

    h₁ = 0 m

    v₂ = 0.75 m/s

    h₂ = 1.65 m

    g = 9.81 m/s²

    Formula

    mgh₁ + 1/2mv₁² = mgh₂ + 1/2mv₂²

    mass is not consider (if we factor mass, it is cancelled)

    gh₁ + 1/2v₁² = gh₂ + 1/2v₂²

    Substitution

    (9.81) (0) + 1/2v₁² = (9.81) (1.65) + 1/2 (0.75) ²

    Simplification

    0 + 1/2v₁² = 16.19 + 0.28

    Solve for v₁

    1/2v₁² = 16.47

    v₁² = 2 (16.47)

    v₁² = 32.94

    Result

    v₁ = 5.74 m/s
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