A visitor to a lighthouse wishes to determine the height of the tower. She ties a spool of thread to a small rock to make a simple pendulum,

Question

A visitor to a lighthouse wishes to determine the height of the tower. She ties a spool of thread to a small rock to make a simple pendulum, which she hangs down the center of a spiral staircase of the tower. The period of oscillation is 9.79 s. The acceleration of gravity is 9.8 m/s 2 . What is the height of the tower

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Ngọc Hoa 5 months 2021-08-21T07:23:41+00:00 1 Answers 8 views 0

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    2021-08-21T07:25:07+00:00

    Answer:

    The height of the tower is 23.786 m

    Explanation:

    Given;

    period of oscillation, t = 9.79 s

    acceleration of gravity, g = 9.8 m/s²

    The period of oscillation is calculated as follows;

    t = 2\pi \sqrt{\frac{h}{g} } \\\\

    where;

    h represents the height of the tower

    g is the acceleration of gravity

    t = 2\pi \sqrt{\frac{h}{g} } \\\\\sqrt{\frac{h}{g} }  = \frac{t}{2\pi} \\\\

    square both sides of the equation;

    (\sqrt{\frac{h}{g} })^2  = (\frac{t}{2\pi} )^2\\\\ \frac{h}{g}  = \frac{t^2}{4\pi ^2} \\\\h = \frac{gt^2}{4\pi ^2} \\\\h =  \frac{9.8*(9.79)^2}{4\pi ^2}\\\\h = 23.786 \ m

    Therefore, the height of the tower is 23.786 m

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