NEM1001: Algebra & Calculucas, Project Ferries Wheel With A River Meanders - Mathematics Assignment Help

Assignment Task

 

PROJECT

SECTION 1: THE FERRIS WHEEL

A Ferris Wheel operates at a theme park. 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 back to the platform is 6x minutes. The process repeats, until the final passenger(s) embark at no later than 10pm each evening (so, a capsule can be filled at 10pm but not later). 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:

The variables a, b and x 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 2 (e.g. if your id is 4567891 then x=8).

Complete the following mathematical analysis, showing all working out.

Task 1:

What is 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 10pm (so, at 10pm, they can) and the first passengers embark at 4pm). Note, it is possible that the final passenger(s) may embark the capsule prior to 10pm, so the answer to this task may not be as easy as 10pm + 6x, in some cases.

Task 4:

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

 

SECTION 2: THE RIVER

A river meanders through a large park as pictured below:

 

The north bank of the river is denoted by the function,

And the south bank is denoted by,

Where,

• a = the last digit of your id plus 5 and then multiplied by 10 (for example, if the last digit is 5, then a = (5+5)*10 = 100).

• b = the second last digit of your id plus 10 and then multiplied by 20 (for example, if the second last digit is 7, then b = (7+10)*20 = 340).

All measurements are in metres, with the park having rectangular dimensions of (a m x b m).

A swimmer starts at point P and it is assumed that the swimmer’s path is not affected by currents or other movements in the river.

Complete the following mathematical analysis, showing all working out.

Task 1:

If the swimmer swims north from point P, find the distance, in metres, the swimmer needs to swim to get to the north bank of the river.

The north bank of the river is denoted by the function,

And the south bank is denoted by,

Where,

• a = the last digit of your id plus 5 and then multiplied by 10 (for example, if the last digit is 5, then a = (5+5)*10 = 100).

• b = the second last digit of your id plus 10 and then multiplied by 20 (for example, if the second last digit is 7, then b = (7+10)*20 = 340).

All measurements are in metres, with the park having rectangular dimensions of (a m x b m).

A swimmer starts at point P and it is assumed that the swimmer’s path is not affected by currents or other movements in the river.

Complete the following mathematical analysis, showing all working out.

Task 1:

If the swimmer swims north from point P, find the distance, in metres, the swimmer needs to swim to get to the north bank of the river.

Task 2:

If the swimmer swims east from point P, find the distance, in metres, the swimmer needs to swim to get to the north bank of the river (Hint: Use a graphics calculator or Online App to assist in the solution to this task).

The north bank of the river is denoted by the function,

And the south bank is denoted by,

Where,

• a = the last digit of your id plus 5 and then multiplied by 10 (for example, if the last digit is 5, then a = (5+5)*10 = 100).

• b = the second last digit of your id plus 10 and then multiplied by 20 (for example, if the second last digit is 7, then b = (7+10)*20 = 340).

All measurements are in metres, with the park having rectangular dimensions of (a m x b m).

A swimmer starts at point P and it is assumed that the swimmer’s path is not affected by currents or other movements in the river.

Complete the following mathematical analysis, showing all working out.

Task 1:

If the swimmer swims north from point P, find the distance, in metres, the swimmer needs to swim to get to the north bank of the river.

Task 2:

If the swimmer swims east from point P, find the distance, in metres, the swimmer needs to swim to get to the north bank of the river (Hint: Use a graphics calculator or Online App to assist in the solution to this task).

Task 3:

Calculate the surface area, using integration, of the river in the park as shown in the diagram above.

Task 4:

A horizontal line is placed through P, as pictured below. This creates ‘no swim’ zones in the river (coloured red).

Calculate the surface area, using integration, of the river in the park as shown in the diagram above.

Task 1:

A horizontal line is placed through P, as pictured below. This creates ‘no swim’ zones in the river (coloured red).

If the swimmer swims east from point P, find the distance, in metres, the swimmer needs to swim to get to the north bank of the river (Hint: Use a graphics calculator or Online App to assist in the solution to this task).

Task 2:

Calculate the surface area, using integration, of the river in the park as shown in the diagram above.

Task 3:

A horizontal line is placed through P, as pictured below. This creates ‘no swim’ zones in the river (coloured red).

 

Q-Calculate the surface area of the ‘no swim’ zones. What is the percentage of the river, in the park, is a ‘no swim’ zone.

 

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