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?

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