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30 July, 03:30

A visitor to a lighthouse wishes to determine the height of the tower. The visitor ties a spool of thread to a small rock to make a simple pendulum, then hangs the pendulum down a spiral staircase in the center of the tower. The period of oscillation is 9.49 s. What is the height of the tower?

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  1. 30 July, 03:49
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    22.38 m

    Explanation:

    Using,

    T = 2π√ (L/g) ... Equation 1

    Where T = period of the oscillation, L = Length of the pendulum,/Height of the tower. g = acceleration due to gravity.

    Make L the subject of the equation

    L = gT² / (4π²) ... Equation 2

    Given: T = 9.49 s, g = 9.8 m/s², π = 3.14

    Substitute into equation 2

    L = 9.8 (9.49²) / (4*3.14²)

    L = 22.38 m

    Hence the height of the tower = 22.38 m
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