High School

A man enters a tall warehouse and notices a long pendulum that nearly reaches from the ceiling to the floor. The pendulum swings back and forth with a period of 26.0 s.

(a) Assuming the pendulum is nearly as long as the warehouse is tall, what is the height of the warehouse (in meters)?

A. 16.9
B. 33.8
C. 66.9
D. 133.8

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.