T^2 = 2ΟL/g
so plug in your numbers to find L
so plug in your numbers to find L
T = 2Οβ(L/g)
so
(T/2Ο)^2 = L/g
T = 2Οβ(L / g)
Where:
T = period of the pendulum (in seconds)
L = length of the pendulum (in meters)
g = acceleration due to gravity (approximately 9.8 m/s^2)
Given that the period T is 6.9 seconds, we can rearrange the formula to solve for L:
L = (T / (2Ο))^2 * g
Now, let's substitute the given values:
L = (6.9 / (2Ο))^2 * 9.8
Calculating this expression, we get:
L β 6.9^2 * 9.8 / (2Ο)^2
L β 47.79 m
Therefore, the length of the bungee cord when Elwin is swinging from it is approximately 47.79 meters.
T = 2Οβ(L/g)
Where:
T is the period (in seconds)
Ο is a mathematical constant (approximately 3.14159)
L is the length of the pendulum (in meters)
g is the acceleration due to gravity (approximately 9.8 m/sΒ²)
In this case, we are given the period T as 6.9 seconds. Let's substitute this value into the formula and solve for L:
6.9 = 2Οβ(L/9.8)
First, let's simplify the equation by dividing both sides by 2Ο:
6.9 / (2Ο) = β(L/9.8)
Now, we can square both sides of the equation to isolate L:
(6.9 / (2Ο))^2 = L/9.8
Simplifying further:
(6.9 / (2Ο))^2 * 9.8 = L
Using a calculator, we can evaluate the left-hand side of the equation:
(6.9 / (2Ο))^2 * 9.8 β 42.205
Therefore, the length of the bungee cord when Elwin is swinging from it is approximately 42.205 meters.