A aerialist on a high platform holds on to a trapeze attached to a sup

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In summary, the problem involves an aerialist on a high platform holding onto a trapeze attached to a support by a 8.2-m cord. The cord makes an angle of 39.8deg with the vertical before the aerialist jumps off. The trapeze is released at the instant it is 0.64 m below its initial height. Using the equation cos(theta) = A/H, the angle θ that the trapeze cord makes with the vertical at this instant can be calculated to be 32.2 deg. The length of the rope remains constant at 8.2 m and by examining the triangles in the attached figure, a better understanding of the solution can be gained.
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cmkc109
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Homework Statement



A aerialist on a high platform holds on to a trapeze attached to a support by a 8.2-m cord. Just before he jumps off the platform, the cord makes an angle α of 39.8deg with the vertical. He jumps, swings down, then back up, releasing the trapeze at the instant it is 0.64 m below its initial height. Calculate the angle θ that the trapeze cord makes with the vertical at this instant.

Homework Equations



cos(theta) = A/H

The Attempt at a Solution



So I found the solution online.
8.2 cos 39.8 = 6.3
6.3 + 0.64 =6.94
cos ^-1 (6.94 / 8.2) = 32.2 deg

However I am not understanding it at all. I don't understand where is the initial position, when the rope is vertical or when the guy is holding on to it?
I have attached the picture , can someone label on the picture or explain it please?

My understanding is, the middle is 8.2m , the right rope is 6.3m, and the left rope is 6.94m
but then the calculation doesn't really make sense.
since if the middle is 8.2, to find l, u should do cos 39.8 = 8.2 / l, and l will be 10.67 instead.
 

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  • #2
The length of the rope is ##l## = 8.2 m. The length of the rope does not change.

Examine some of the triangles shown in the attached figure.
 

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  • Trapeze.jpg
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  • #3
very helpful, thank you very much.
 

Related to A aerialist on a high platform holds on to a trapeze attached to a sup

1. How does an aerialist stay balanced on a high platform while holding onto a trapeze?

An aerialist uses their core muscles and body awareness to maintain balance while on a high platform. They also rely on training and practice to develop the strength and control needed for this type of performance.

2. What safety measures are in place for an aerialist performing on a high platform?

Safety is a top priority for aerial performers. The platform and rigging are carefully inspected and secured before each performance. The aerialist also wears a safety harness and is trained in proper safety techniques, such as how to properly grip the trapeze and how to fall safely if needed.

3. How does the trapeze stay attached to the sup (support structure)?

The trapeze is securely attached to the sup using a combination of clamps, carabiners, and rigging equipment. These attachments are carefully checked and maintained to ensure the safety of the performer.

4. What skills and training are needed to perform as an aerialist on a high platform?

Aerialists need a combination of strength, flexibility, and body awareness to perform on a high platform. They also undergo extensive training in aerial techniques, safety procedures, and choreography. Many aerialists also have a background in dance or gymnastics.

5. What is the purpose of an aerialist performing on a high platform?

The purpose of an aerialist performing on a high platform is to create a visually stunning and thrilling performance for the audience. It requires a high level of skill and control to perform on a high platform, making it a captivating and impressive spectacle.

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