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A water balloon is catapulted into the air from the top of a building. The height, h(x), in metres, of the balloon after t seconds is h(x)=-5t^2+30t+10.

What are the domain and range of this function?

When will the ball reach a height of 30 cm?

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Sixta Kovacek
Sixta KovacekLv2
26 Feb 2019

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Joey Tang
Joey Tang
Bachelor’s Degree in Chemistry from McMaster University
8 May 2020

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A golfer hits a golf ball with an initial velocity of 50 m/s. The height of the ball, h in metres, after t seconds, can be modelled by the function
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the quadratic function h(t)=-16.1t^2+150 models a ball's height, in feet, over time, in seconds, after it is dropped from a 15 story building.
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Mr and Mrs Spin operate a Ferris Wheel at various shows and carnivals. A passenger sits in a capsule and enjoys the ride and views. Below is a diagram showing their magnificent wheel:

Passengers embark and disembark the capsule from the platform (a maximum of 6 passengers are allowed at any given time). The time for a passenger to enter the capsule and return to the platform is 6x minutes. The process repeats until the final passenger(s) embark at no later than 10 pm each evening. The Ferris Wheel runs in an anti-clockwise direction. The height h, in metres, from the ground to a capsule, is measured from the ground to the ball on top of any capsule. It is modelled by 𝒉(𝒕) = 𝒂 − 𝐛cos (𝝅/ 𝟑) A passenger pays 3y dollars for a ride on the wheel. The variables a, b, x and y are as follows: § a is equal to 14 (i.e. a=14) § b is equal to the last digit of your student id plus 2 (e.g. if your id is 4567891 then b=3). § x is equal to the third digit of your id plus 3 (e.g. if your id is 4567891 when x=9). § y is equal to the month that you are born plus 6 (e.g. if you are born in July then y=13). Mr and Mrs Spin would like you to do the following mathematical analysis and present the results in a report for their consumption.

Task 1:

What are the minimum and maximum height of a capsule on the Ferris Wheel?

Task 2:

Determine the heights of each of the capsules on the Ferris Wheel while passengers either embark or disembark a capsule. Present these heights in table form, with appropriate labelling.

Task 3:

Determine the time when the final passenger(s) will disembark the capsule and the Ferris Wheel cease for the evening (remember that the final passengers will embark no later than 10 pm). Note, it is possible that the final passenger(s) may embark the capsule prior to 10 pm, so the answer to this task may not be 10 pm + 6x.

 

Task 4:

Evaluate the number of capsules that will have a passenger(s) embark for any day, given the Ferris Wheel will commence at 4 pm and the time for passenger(s) to embark and disembark is considered negligible.

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