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14 March, 03:12

If a roller coaster car had 40,000 J of gravitational potential energy when at rest on the top of a hill how much kinetic energy does it have when it is 3/4 of the way down the hill

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  1. 14 March, 03:26
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    K. E = 30,000 J

    Explanation:

    Given,

    The potential energy of the roller coaster car, P. E = 40000 J

    The kinetic energy at height h/4, K. E = ?

    According to the law of conservation of energy, the total energy of the system is conserved.

    At height 'h', the total energy is,

    P. E = mgh

    K. E = 0

    At height 'h/4', the total energy is

    P. E + K. E = mgh

    P. E = mgh/4

    K. E = 1/2 mv²

    Therefore,

    mgh/4 + 1/2 mv² = mgh

    gh/4 + v²/2 = gh

    Hence,

    v² = 3gh/2

    Substituting in the K. E equation

    K. E = 1/2 mv²

    = 1/2 m (3gh/2)

    = 3/4 mgh

    = 3/4 x 40000

    = 30000 J

    Hence, the K. E of the roller coaster car is, K. E = 30000 J
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