- #1

songoku

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- Homework Statement
- The data below shows the height and speed of a roller coaster ride when it moves through the circular part of a track having diameter of 160 m.

The height is measured in meter and speed in meter per second. The bottom of the circular track is 20 meter from ground.

Calculate the lower and upper limit for the time for the roller coaster to travel from a height of 100 meter to a height of 20 meter. State the assumption and additional information (if needed) to be able to calculate the time

- Relevant Equations
- Hyperbolic Function

Riemann Sum

height from ground | speed |

100 | 40 |

80 | 48 |

60 | 60 |

40 | 72 |

20 | 80 |

I tried to plot the points (speed on x-axis and height on y axis) and I got more or less like a straight line but I am not sure whether the graph would help to calculate the upper and lower limit of the time.

I also tried to use Riemann sum but just stuck because as far as I know, Riemann sum is used to calculate area under curve while for this question the time is not the area under the curve.

I am also not sure what assumption I need to make. Since this is math question, I don't think the assumption will be physics-related, such as frictionless track (I even used conservation of energy for this question and got nowhere). And I don't really understand about "additional information" part, basically because I have no idea how to calculate the time so I don't know whether the data given is sufficient or not

Please give me hint to start. Thanks