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13 November, 12:19

The jumper has a mass of 50 kg, and the bridge's height above the river is 150 m. The rope has an unstretched length of 11 m and stretches a distance of 4 m before bringing the jumper to a stop. Determine the maximum speed of the jumper and the spring constant of the rope. In your calculation, use g

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  1. 13 November, 14:36
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    The maximum speed of the jumper is 54.2m/s

    The spring constant of the rope is

    K=9.19KN/m

    Explanation:

    Step one

    According to hook's law the applied force F is proportional to the extension e provided the elasticity is maintained

    Step two

    Given that

    mass = 50kg

    Height of bridge h=150m

    Extention e=4m

    Step three

    To determine the maximum speed of the jumper

    Since he is going with gravity we assume g=9.81m/s²

    And we apply the equation of motion

    V²=U²+2gh

    where u = initial velocity of the jumper = 0

    h=height of bridge

    Step four

    Substituting we have

    V²=0²+2*9.81*150

    V²=2943

    V=√2943

    V=54.2m/s

    Step five

    To solve for the spring constant

    We have to equate to potential energy of the jumper to the energy stored in the spring

    Potential energy of the jumper = mgh

    Energy stored in the spring = 1/2ke²

    Hence mgh=1/2ke²

    Making k subject of formula we have

    K=2mgh/e²

    Substituting our data into the expression we have

    K=2*50*9.81*150/4²

    K=147150/16

    K=9196.9N/m

    K=9.19KN/m
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