The time for a swing to move forward and backwards is determined by this formula.
T=2pi sqrt L/9.8. T is the time, in seconds,taken for the swing to move through one complete cycle. L is the length of rope supporting the swing.
Determine the length of the rope supporting a swing that takes 3.4 seconds to move through one cycle. Round to nearest tenth of a metre.
Please help thank you
To determine the length of the rope supporting the swing, we can rearrange the formula to solve for L. The formula is given as:
T = 2π √(L/9.8)
We are given that T = 3.4 seconds. Substituting this value into the formula:
3.4 = 2π √(L/9.8)
To solve for L, we need to isolate L. First, divide both sides of the equation by 2π:
3.4 / (2π) = √(L/9.8)
Next, square both sides of the equation to eliminate the square root:
(3.4 / (2π))^2 = L/9.8
Now, multiply both sides of the equation by 9.8 to solve for L:
9.8 * (3.4 / (2π))^2 = L
Using a calculator, perform the calculations:
L = 9.8 * (3.4 / (2 * 3.14159))^2
L = 9.8 * (3.4 / 6.28318)^2
L = 9.8 * (0.54022)^2
L = 9.8 * 0.29236
L = 2.866 km
Therefore, the length of the rope supporting the swing that takes 3.4 seconds to move through one cycle is approximately 2.9 meters (rounded to the nearest tenth of a meter).
just plug in your numbers:
3.4 = 2π√(L/9.8)
Just solve for L