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2 June, 10:07

A 165g arrow is shot straight up into the air with a speed of 16m/s reaches a maximum height of 12.0612m. a. Find the initial kinetic energy. The acceleration of gravity is 9.8m/s^2.

b. Find the potential energy at its highest position.

c. Find the magnitude of the energy lost due to air resistance.

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  1. 2 June, 12:22
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    a. 21.12 J

    b. 19.50 J

    c. 1.62 J

    Explanation:

    Kinetic Energy: this is the energy of a body due to motion.

    it is represented mathematically as

    Ek = 1/2mv² ... Equation 1

    Where Ek = kinetic energy, m = mass of the arrow, v = velocity of the arrow

    Potential Energy: This is the energy of a body due to position.

    It is represented mathematically as

    EP = mgh ... Equation 2

    Ep = potential Energy, h = height, g = acceleration due to gravity.

    (a) The initial kinetic energy.

    using Equation 1,

    Ek = 1/2mv²

    given: m = 165 g = 0.165 kg, v = 16 m/s.

    Substituting these values into equation 1

    Ek = 1/2 (0.165) (16) ²

    Ek = 21.12 J.

    (b) The potential energy at its highest position

    Using Equation 2

    Ep = mgh

    given: m = 165 g = 0.165 kg, h = 12.0612 m, g = 9.8 m/s²

    Substituting these values into equation 2

    Ep = 0.165 (12.0612) (9.8)

    Ep = 19.50 J

    (c) Energy lost due to air resistance

    = Initial kinetic energy - potential energy at the highest position

    EL = Ek - Ep

    Where EL = energy lost.

    EL = 21.12 - 19.50

    EL = 1.62 J
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