An aerialist on a high platform holds onto a trapeze attached to a support by a 9.9-meter cord. Just before he jumps off the platform, the cord makes an angle of 36° with the vertical. He jumps, swings down, then back up, releasing the trapeze at the instant it is 0.70 meters below its initial height.

Calculate the angle \( \theta \) that the trapeze cord makes with the vertical at this instant.

Question

26-09-2024
Physics

High School

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An aerialist on a high platform holds onto a trapeze attached to a support by a 9.9-meter cord. Just before he jumps off the platform, the cord makes an angle of 36° with the vertical. He jumps, swings down, then back up, releasing the trapeze at the instant it is 0.70 meters below its initial height.

Calculate the angle \( \theta \) that the trapeze cord makes with the vertical at this instant.

Answer :

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SadieSharoff12 SadieSharoff12 · Answer 1 · 2024-05-25T14:52:02-04:00

Final answer:

The problem involves calculating a new angle in a pendulum system after the aerialist jumps, based on the initial angle and the point of release of the trapezium. This is solved using basic trigonometry and physics concepts.

Explanation:

In this physics problem, we are trying to calculate the new angle that the trapeze cord makes with the vertical after the aerialist jumps off. We know from the problem that the initial angle was 36° and that the aerialist releases the trapeze at a point 0.70 m below its initial height. First, we need to calculate the difference in the height of the trapeze using trigonometry. The formula to calculate this height is h = L * (1 - cosθ), where L is the length of the rope and θ is the angle it makes. By substituting and simplifying this equation, we can solve for θ.

Let's plug in the given values: 0.7 m = 9.9 m * (1 - cos θ). Solving this equation gives us the new angle θ which the cord makes with the vertical when the aerialist releases it. In solving problems such as these, the concept of angles in a pendulum-like system and basic trigonometry are essential.

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