Question

Noah plans on using a pendulum to determine the height of a tower. He attaches a mass to the end of a thin cord hanging from the tower's ceiling (let's assume the cord almost touches the ground). Noah determines the period of oscillation to be 12 s. How high is the tower?

Answer 1

The height of the tower is 35.75 m.

What is height?

Height is the vertical distance between two points.

To calculate the height of the tower, we use the formula below.

Formula:

• T = 2π√(L/g)............ Equation 1

Where:

• T = Period of oscillation
• π = Pie
• L = height of the tower
• g = acceleration due to gravity.

From the question,

Given:

• T = 12 s
• g = 9.8 m/s²
• π = 3.14

Substitiute these values into equation 1 and solve for L

• 12 = 2(3.14)√(L/9.8)
• 12 = 6.28√(L/9.8)
• √(L/9.8) = 12/6.28
• √(L/9.8) = 1.91
• L/9.8 = (1.91)²
• L/9.8 = 3.6481
• L = 9.8×3.6481
• L = 35.75 m

Hence, the height of the tower is 35.75 m.

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