The Parametric Vector Form of the Position of a Roller $\vec { r } ( t ) = 30 \sin ( t ) \vec { i } + 30 \cos ( t ) \vec { j } + 15 \cos ( t ) \vec { k }$

question 37

Essay

The parametric vector form of the position of a roller coaster is $\vec { r } ( t ) = 30 \sin ( t ) \vec { i } + 30 \cos ( t ) \vec { j } + 15 \cos ( t ) \vec { k }$ Answer the following questions about the ride.
(a)The scariest point of the ride is when it is traveling fastest.For which value of t > 0 does this occur first?
(b)Does the velocity vector of the roller coaster ever point directly downward?

---

Definitions:

Social Welfare

Organized efforts and policies aimed at providing assistance and support to individuals and families in need.

Civil Liberties

Fundamental rights and freedoms protected by law from governmental interference, including freedom of speech and religion.

Foreign Policy

A government's strategy in dealing with other nations, including diplomacy, trade agreements, and military actions.

Political Socialization

The process by which individuals learn and frequently adopt the political culture and values of their society.