Here are the essential concepts you must grasp in order to answer the question correctly.
Conservation of Energy
The principle of conservation of energy states that the total energy in a closed system remains constant. In this scenario, the kinetic energy of the student when running is converted into gravitational potential energy as he swings upward on the rope. Understanding this concept is crucial for determining the height reached and the angle at which the student releases the rope.
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Conservation Of Mechanical Energy
Kinematics of Circular Motion
When the student swings on the rope, he undergoes circular motion. The kinematics of circular motion involves analyzing the forces and motion of an object moving along a circular path. This concept helps in understanding how the angle θ can be determined based on the radius of the swing and the height achieved at the point of release.
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Trigonometric Relationships
Trigonometric relationships are essential for relating the angles and sides of triangles. In this problem, the angle θ can be found using trigonometric functions, such as sine or cosine, which relate the height of the swing to the length of the rope. This mathematical relationship is key to solving for the angle at which the student releases the rope.
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