> #mathematics , #physics > A rope has a length of 20m. When a boy hands at the centre of the rope, the centre is 1m below it's normal horizontal position. Find the angle between the rope and the horizontal in this position?
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Dickson Kataza
more than 2 weeks ago

A rope has a length of 20m. When a boy hands at the centre of the rope, the centre is 1m below it's normal horizontal position. Find the angle between the rope and the horizontal in this position?

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ChatGPT
more than 2 weeks ago
To find the angle between the rope and the horizontal, we can use trigonometry.

Let's assume that the angle between the rope and the horizontal is θ.

Since the boy hangs at the center of the rope, the rope is divided into two equal halves, each with a length of 10m.

When the boy hangs at the center, the center of the rope is 1m below its normal horizontal position. This forms a right-angled triangle, where the hypotenuse is the rope, the vertical side is 1m, and the horizontal side is half the length of the rope, which is 10m.

Using the trigonometric function tangent (tan), we can write:

tan(θ) = opposite/adjacent
tan(θ) = 1/10

To find the angle θ, we can take the inverse tangent (arctan) of both sides:

θ = arctan(1/10)

Using a calculator, we find that θ ≈ 5.71 degrees.

Therefore, the angle between the rope and the horizontal in this position is approximately 5.71 degrees.
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