In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole. With what m

Question

In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must the athlete leave the ground in order to lift his center of mass 1.80 m and cross the bar with a speed of 0.80 m/s?

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Jezebel 3 weeks 2021-08-26T18:37:19+00:00 1 Answers 0 views 0

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    2021-08-26T18:39:00+00:00

    Answer:

    6.0 m/s

    Explanation:

    According to the law of conservation of energy, the total mechanical energy (potential, PE, + kinetic, KE) of the athlete must be conserved.

    Therefore, we can write:

    KE_i+PE_i =KE_f+PE_f

    or

    \frac{1}{2}mu^2+0=\frac{1}{2}mv^2+mgh

    where:

    m is the mass of the athlete

    u is the initial speed of the athlete (at the bottom)

    0 is the initial potential energy of the athlete (at the bottom)

    v = 0.80 m/s is the final speed of the athlete (at the top)

    g=9.8 m/s^2 is the acceleration due to gravity

    h = 1.80 m is the final height of the athlete (at the top)

    Solving the equation for u, we find the initial speed at which the athlete must jump:

    u=\sqrt{v^2+2gh}=\sqrt{0.80^2+2(9.8)(1.80)}=6.0 m/s

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