the time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below. (…

the time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below. ( f(l)=2pisqrt{\frac{l}{32}} ), where ( l ) is the length of the pendulum in feet. what is the approximate length of a pendulum that takes ( 2.4pi ) seconds to swing back and forth? 1.72 ft 3.05 ft 38.40 ft 46.08 ft

the time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below. ( f(l)=2pisqrt{\frac{l}{32}} ), where ( l ) is the length of the pendulum in feet. what is the approximate length of a pendulum that takes ( 2.4pi ) seconds to swing back and forth? 1.72 ft 3.05 ft 38.40 ft 46.08 ft

Answer

  1. First, set up the equation:
    • We are given the formula (T = 2\pi\sqrt{\frac{l}{32}}), where (T) is the time - period of the pendulum's swing and (l) is the length of the pendulum.
    • We know that (T = 2.4\pi) seconds. So, we substitute (T) into the formula:
      • (2.4\pi=2\pi\sqrt{\frac{l}{32}}).
  2. Then, solve for (l):
    • First, divide both sides of the equation by (2\pi):
      • (\frac{2.4\pi}{2\pi}=\sqrt{\frac{l}{32}}).
      • Simplifying the left - hand side gives (1.2=\sqrt{\frac{l}{32}}).
    • Next, square both sides of the equation to get rid of the square - root:
      • ((1.2)^2=\frac{l}{32}).
      • So, (1.44=\frac{l}{32}).
    • Then, multiply both sides by 32 to solve for (l):
      • (l = 1.44\times32=46.08) feet.

Answer: 46.08 ft