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Answer :
Final answer:
The angle θ that the trapeze cord makes with the vertical when it is 0.61 m below its initial height is calculated using trigonometry, resulting in an angle of 47.5°. So, the correct option is D.
Explanation:
The student's question involves calculating the angle θ that the trapeze cord makes with the vertical at the instant it is 0.61 m below its initial height. To solve this problem, the principles of physics, specifically the conservation of energy and trigonometry, are used. Initially, the potential energy is all converted into kinetic energy as the aerialist falls, and then back into potential energy when the cord makes the angle with the vertical.
Since the lengths of the trapeze cord and the height difference are known, we can use trigonometry to calculate the angle. The initial vertical height (h1) can be found by the equation h1 = L - L*cos(α), where L is the length of the cord and α is the initial angle with the vertical. The angle at the new height (h2 = h1 - 0.61m) can be determined by rearranging the equation to solve for the new angle (θ).
Using the trigonometric relationship cos(θ) = (L - h2) / L, we can find the angle θ in terms of known quantities. Plugging the values into the equation, it will yield the appropriate result. Based on the calculations using the given values, the angle θ that the trapeze cord makes with the vertical at the moment when it is 0.61 m below its initial height is 47.5°. Therefore, the correct answer is Option D: 47.5°.
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