Question

What is the approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth?

Answer 1

Answer:

The approximate length of the pendulum is 46.08 ft

Step-by-step explanation:

The time (t) of pendulum oscillation is given as;

$t = 2 \pi\sqrt{\frac{L}{g} }$

where;

L is the length of the pendulum

g is acceleration due to gravity = 9.8 m/s² = 32.15 ft/s²

t is the time given as 2.4 π seconds

From the equation above, make L the subject of the formula;

$t = 2 \pi\sqrt{\frac{L}{g} } \\\\\frac{t}{2\pi} = \sqrt{\frac{L}{g} }\\\\(\frac{t}{2\pi} )^2 =\frac{L}{g} \\\\L = g*(\frac{t}{2\pi} )^2\\\\L = 32.15*(\frac{2.4 \pi}{2\pi} )^2\\\\L = 32.15 *1.44\\\\L = 46.296 \ ft$

Therefore, the approximate length of the pendulum is 46.29 ft

The closest option is 46.08 ft