Final answer:
By observing that two full swings take 10.0 seconds and using the period formula for a pendulum, the length of the swing is estimated to be approximately 6.21 meters.
Step-by-step explanation:
To estimate the length of the swing from the observation that a child completes two full swings in 10.0 seconds, we can use the physics of pendulum motion.
The time for one complete back-and-forth motion is called the period (T).
The observed period is 5.0 seconds per swing, since two swings took 10.0 seconds.
The formula for the period (T) of a pendulum where L is the length and g is the acceleration due to gravity (approximately 9.81 m/s2) is:
T = 2π√(L/g)
Rearranging the formula to solve for L, we get:
L = (T2g)/(4π2)
By substituting in the values T = 5.0 s and g = 9.81 m/s2, we can calculate the length (L) of the swing.
L = (5.02 × 9.81)/(4π2)
L = (25.0 × 9.81)/(4×(9.8696))
L = (245.25)/(39.4784)
L ≈ 6.21 meters
Therefore, the estimated length of the tire swing is approximately 6.21 meters.