Suppose the outer edge of a playground slide is in the shape of a helix of radius 10.5 meters. The slide has a height of 2 meters and makes one complete revolution from top to bottom. Find a vector-valued function for the helix.
A) $\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 10.5 \sin t \mathbf { j } + t \mathbf { k } , \quad 0 \leq t \leq 4 \pi$
B) $\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 10.5 \sin t \mathbf { j } + \frac { 1 } { \pi } t \mathbf { k } , \quad 0 \leq t \leq 2 \pi$
C) $\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 2 \sin t \mathbf { j } + \frac { 1 } { \pi } t \mathbf { k } , \quad 0 \leq t \leq 2 \pi$
D) $\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 10.5 \sin t \mathbf { j } + \frac { 1 } { \pi } t \mathbf { k } , \quad 0 \leq t \leq 4 \pi$
E) $\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 2 \sin t \mathbf { j } + t \mathbf { k } , \quad 0 \leq t \leq 4 \pi$

Question

Suppose the outer edge of a playground slide is in the shape of a helix of radius 10.5 meters. The slide has a height of 2 meters and makes one complete revolution from top to bottom. Find a vector-valued function for the helix. 
A) $\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 10.5 \sin t \mathbf { j } + t \mathbf { k } , \quad 0 \leq t \leq 4 \pi$
B) $\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 10.5 \sin t \mathbf { j } + \frac { 1 } { \pi } t \mathbf { k } , \quad 0 \leq t \leq 2 \pi$
C) $\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 2 \sin t \mathbf { j } + \frac { 1 } { \pi } t \mathbf { k } , \quad 0 \leq t \leq 2 \pi$
D) $\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 10.5 \sin t \mathbf { j } + \frac { 1 } { \pi } t \mathbf { k } , \quad 0 \leq t \leq 4 \pi$
E) $\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 2 \sin t \mathbf { j } + t \mathbf { k } , \quad 0 \leq t \leq 4 \pi$

Quizplus · Accepted Answer

The correct vector-valued function for a helix with a radius of 10.5 meters and a height of 2 meters over one complete revolution (2π radians) is given by $\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 10.5 \sin t \mathbf { j } + \frac { 1 } { \pi } t \mathbf { k }$. This function correctly models the circular motion in the xy-plane with a radius of 10.5 and a linear increase in the z-direction such that the height increases by 2 meters over the interval $0 \leq t \leq 2 \pi$, which corresponds to one complete revolution.

Suppose the Outer Edge of a Playground Slide Is in the Shape