Chapter 12.1, Problem 39SR

(a)

To determine

To calculate: Distance travelled by the roller coaster to get to the top of the ride.

Answer to Problem 39SR

Distance travelled by the roller coaster to get on top = $415.8\text{ ft}$

Explanation of Solution

Given information:

The following figure:

  

Formula used:

The following Pythagoras theorem:

  ${\text{hypotenuse}}^2={\text{adjacent}}^2+{\text{opposite}}^2$

Calculation:

According to the given diagram:

  $\begin{array}{l}\text{In }\Delta ABD,\\ \text{hypotenuse}=AB\\ \text{adjacent}=BD\\ \text{opposite}=AD\end{array}$

  $AB$ is calculated as:

  $\begin{array}{l}A{B}^2=B{D}^2+A{D}^2 [\text{Pythagoras therorem]}\\ $ ={(360)}^2+{(208)}^2[\text{Substitute]}$=129600+43264 [\text{Find square]}\\ =172864 [\text{Add]}\\ AB\approx 415.8 [\text{Find square root]}\end{array}$

Distance travelled by the roller coaster to get on top = $AB\text{ = }415.8\text{ ft}$

(b)

To determine

To calculate: Distance travelled by the roller coaster on the downhill track.

Answer to Problem 39SR

Distance travelled by the roller coaster on the downhill track = $\text{212}\text{.6 ft}$

Explanation of Solution

Given information:

The following figure:

  

Formula used:

The following Pythagoras theorem:

  ${\text{hypotenuse}}^2={\text{adjacent}}^2+{\text{opposite}}^2$

Calculation:

According to the given diagram:

  $\begin{array}{l}\text{In }\Delta ADC,\\ \text{hypotenuse}=AC\\ \text{adjacent}=DC\\ \text{opposite}=AD\end{array}$

  $AB$ is calculated as:

  $\begin{array}{l}A{C}^2=D{C}^2+A{D}^2 [\text{Pythagoras therorem]}\\ $ ={(44)}^2+{(208)}^2[\text{Substitute]}$=1936+43264 [\text{Find square]}\\ =45200 [\text{Add]}\\ AC\approx 212.6 [\text{Find square root]}\end{array}$

Distance travelled by the roller coaster on the downhill track = $AC\text{ = 212}\text{.6 ft}$