Swinging Angle = 30° Swinging on a Rope: How Far Does He Go?

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In summary, a man is attempting to swing from a 15 m high cliff on a 12 m long rope. He lets go when the rope is 30° from the horizontal on the other side, resulting in a total swing angle of 150°. The problem is to determine how far he lands from the cliff. The solution requires using a circle tangential speed formula and considering conservation laws.
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AdsBerger
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Homework Statement



A man is trying to swing from a 15 m high cliff on a 12 m long rope. (the rope is horizontal at the start) He let's go when the rope is 30° degrees from the horizontal of the other side. (totaled swung angle is 150°.

How far does he go from the cliff?

Homework Equations


I suppose you would use a circle tangentle speed formula, not too sure.



The Attempt at a Solution



The first part of the problem to calculate the speed of of the launch is where i am having trouble.

___& --------------O
|
|
| *X* is where here he let's go X (30°)
|________________________________________________x__________x_____x_ Where
does he land, how far from the cliff.

Circle Radius = r = 12 m
 
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  • #2
What conservation laws might help?
 

1. How is the swinging angle of 30° calculated?

The swinging angle of 30° is calculated using trigonometric functions, specifically the sine function. It is the ratio of the opposite side (height of the swing) to the hypotenuse (length of the rope).

2. Does the length of the rope affect the swinging distance?

Yes, the length of the rope does affect the swinging distance. A longer rope allows for a wider swing arc, resulting in a farther distance traveled.

3. Is air resistance a factor in determining the swinging distance?

Yes, air resistance does play a role in determining the swinging distance. The greater the air resistance, the more it will slow down the swinging motion and decrease the distance traveled.

4. Are there any other factors that may affect the swinging distance?

Other factors that may affect the swinging distance include the mass and weight of the person on the swing, the force applied to the swing, and the surface material of the swing seat.

5. Can the swinging angle of 30° be adjusted to maximize the swinging distance?

Yes, the swinging angle of 30° can be adjusted to maximize the swinging distance. However, the optimal swinging angle may vary depending on the individual's strength, weight, and other factors. Experimentation may be necessary to find the best angle for maximum distance.

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