the period ( t ) (in seconds) of a pendulum is given by ( t = 2pisqrt{(\frac{l}{32})} ), where ( l ) stands…

the period ( t ) (in seconds) of a pendulum is given by ( t = 2pisqrt{(\frac{l}{32})} ), where ( l ) stands for the length (in feet) of the pendulum. if ( pi = 3.14 ), and the period is 9.42 seconds, what is the length? the length of the pendulum is ______ feet. the solution is

the period ( t ) (in seconds) of a pendulum is given by ( t = 2pisqrt{(\frac{l}{32})} ), where ( l ) stands for the length (in feet) of the pendulum. if ( pi = 3.14 ), and the period is 9.42 seconds, what is the length? the length of the pendulum is ______ feet. the solution is

Answer

Explanation:

Step1: Substitute the given values into the formula

Given (T = 9.42) and (\pi=3.14), the formula (T = 2\pi\sqrt{\frac{L}{32}}) becomes (9.42=2\times3.14\sqrt{\frac{L}{32}}). First, simplify (2\times3.14 = 6.28). So, (9.42 = 6.28\sqrt{\frac{L}{32}}).

Step2: Solve for (\sqrt{\frac{L}{32}})

Divide both sides of the equation (9.42 = 6.28\sqrt{\frac{L}{32}}) by (6.28). (\sqrt{\frac{L}{32}}=\frac{9.42}{6.28}). Calculate (\frac{9.42}{6.28}=1.5). So, (\sqrt{\frac{L}{32}} = 1.5).

Step3: Solve for (L)

Square both sides of the equation (\sqrt{\frac{L}{32}} = 1.5). We get (\frac{L}{32}=1.5^{2}). Since (1.5^{2}=2.25), then (L = 2.25\times32). Calculate (2.25\times32=(2 + 0.25)\times32=2\times32+0.25\times32=64 + 8=72).

Answer:

(72)