A Particle Is Traveling Along a Helix Whose Vector Equation $\mathbf { r } ( t ) = \left\langle R _ { 1 } \cos \alpha t , R _ { 2 } \sin \alpha t , \beta t \right\rangle$

question 62

Essay

A particle is traveling along a helix whose vector equation is given by $\mathbf { r } ( t ) = \left\langle R _ { 1 } \cos \alpha t , R _ { 2 } \sin \alpha t , \beta t \right\rangle$ , where $R _ { 1 } \geq R _ { 2 }$ . Find its maximum and minimum speeds.

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Definitions:

Exclusionary Rule

A legal principle in the United States that prohibits the use of evidence collected or analyzed in violation of the defendant's constitutional rights.

Fourth Amendment

Part of the U.S. Constitution that protects individuals against unreasonable searches and seizures by the government.

U.S. Constitution

The foundational document of the United States government, outlining the structure, functions, and powers of its three branches and the rights of its citizens.

Duress

Compulsion by threat or force; coercion that makes someone act against their will.