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Answer :
Final answer:
The warehouse's height, based on the pendulum's period of 26.0 seconds, is approximately 66.9 meters. The correct answer is option c.
Explanation:
To determine the height of the warehouse based on the pendulum's period, we can use the formula for the period of a simple pendulum, which is
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 9.8 m/s²).
According to the given information, the pendulum has a period (T) of 26.0 seconds. Rearranging the formula to solve for L, we get
L = (T/(2π))² × g.
Plugging the values into the equation, we get:
L = ((26.0 / (2 × 3.14159))² × 9.8 m/s²
≈ 33.8 meters.
Considering that the pendulum nearly reaches from the ceiling to the floor, the height of the warehouse would be approximately double the length of the pendulum, which gives us:
H = 2L
≈ 2 × 33.8 meters
≈ 67.6 meters.
From the options provided, the closest value to our calculation is 66.9 meters, which suggests that the correct answer would be Option c, 66.9 meters.
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