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30 July, 14:27

A sprinter must average 24.0 mi/h to win a 100-m dash in 9.30 s. What is his wavelength at this speed if his mass is 84.5 kg?

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Answers (2)
  1. 30 July, 14:56
    0
    Answer: 7.31*10^-37

    Explanation:

    Given

    Speed of sprinter, v = 24 mi/h

    Distance to run, d = 100 m

    Time needed for the run, t = 9.3 s

    Mass of sprinter, m = 84.5 kg

    Wavelength of sprinter, λ = ?

    To solve this question, we would be using De Broglie's wavelength.

    λ = h/mv, where

    λ = wavelength

    h = Planck's constant = 6.63*10^-34 m²kg/s

    m = mass

    v = velocity

    To start with, we convert the speed of the sprinter from mi/h to m/s

    v = 24 mi/h

    1 mile = 1609 m

    1 hour = 3600 s

    24 mi/h = (24 * 1609) / 3600

    24 mi/h = 38616 / 3600

    24 mi/h = 10.73 m/s

    λ = 6.63*10^-34 / 84.5 * 10.73

    λ = 6.63*10^-34 / 906.685

    λ = 7.31*10^-37

    Therefore, the wavelength of the sprinter is 7.31*10^-37 m
  2. 30 July, 17:09
    0
    Wavelength λ = 7.31 * 10^-37 m

    Explanation:

    From De Broglie's equation;

    λ = h/mv

    Where;

    λ = wavelength in meters

    h = plank's constant = 6.626*10^-34 m^2 kg/s

    m = mass in kg

    v = velocity in m/s

    Given;

    v = 24 mi/h

    Converting to m/s

    v = 24mi/h * 0.447 m/s * 1 / (mi/h)

    v = 10.73m/s

    m = 84.5kg

    Substituting the values into the equation;

    λ = (6.626*10^-34 m^2 kg/s) / (84.5kg * 10.73m/s)

    λ = 7.31 * 10^-37 m
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