Final answer:
The length of a pendulum that takes 1.5 seconds to swing back and forth is approximately 1.8 feet, calculated using the formula for the period of a simple pendulum and the approximation that the acceleration due to gravity is 9.81 m/s^2.
Step-by-step explanation:
To find the approximate length of a pendulum that takes 1.5 seconds to swing back and forth, we can use the formula for the period (T) of a simple pendulum: T = 2π√(l/g), where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.81 m/s2 or 32.2 ft/s2 on Earth). We need to solve this formula for l to find the length when the period T is given as 1.5 seconds.
Rearranging the formula to solve for l gives us l = (T/2π)² × g. Plugging in T = 1.5 seconds and g = 9.81 m/s2, we get:
l = (1.5/2π)² × 9.81 m/s2
Calculating this, we find the length l to be approximately 0.56 meters, which is about 1.84 feet when converted to feet (1 meter ≈ 3.28 feet). To find the length to the nearest tenth of a foot, we have:
1.84 feet ≈ 1.8 feet (to the nearest tenth).
Therefore, the approximate length of a pendulum that takes 1.5 seconds to swing back and forth is 1.8 feet.