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

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To determine how far a man swings from a 15 m high cliff on a 12 m rope, he releases the rope at a 30° angle from the horizontal, resulting in a total swing angle of 150°. The key to solving this problem lies in calculating the tangential speed at the point of release. Conservation of energy principles can be applied to find the speed at the lowest point of the swing. From this speed, projectile motion equations can be used to calculate the horizontal distance traveled after he lets go. The final distance from the cliff can then be determined using these calculations.
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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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What conservation laws might help?
 

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