The ACME plans provide the following information: The roller coaster is to be built in the shape of a sinusoid (see the figure provided on the following page). The high and low points on the track are to be separated by 50 meters horizontally and by 30 meters vertically. The low point is to be 3 meters below the ground.
Wile E. Coyote
Genius Extraordinaire! Trey Cox and Scott Adamson ©2000
3
The vertical timbers are to be spaced every 2 meters, starting at the base of the mountain (x = 0) and ending where the track goes below the ground. The horizontal timbers are to be spaced every 3 meters.
Don’t forget that there has to be a front and backside to the roller coaster (or it would just fall over!).
At each intersection of horizontal and vertical timber, there is a 1 meter timber tie between the two sets of coinciding supporting timbers.
Timber supports will cost $3.00 a meter.
Since the ACME kit comes with the steel rails and cart but not the timber supports, please provide me with the following information:
So I can try to understand the mathematics behind your calculations give me a general formula for the sinusoidal roller coaster track.
What is the length of the vertical timber I need at the high point? What is the length of the horizontal timber I need that will be 24 meters above the ground?
Where will the track first go below ground? Where will it first come back out from below ground level? What are the lengths of each horizontal and vertical timber support?
What is total length of all the timber supports so that I will know how much to purchase?
How much money will it cost me to purchase the timber supports? Finally, with my storied history of accidents, I am a little concerned about heights. Can you give me an estimate of how steep the roller coaster will be at its steepest point?
It has been so long since I have had the delicacy of Road Runner Delight, I would appreciate your response by _________________. This will give me enough time so I can make preparations for the best meal I have had in years and invite the whole den over!
I anxiously await your reply…, Wile E. Coyote (Carnivorous Vulgaris)
P.S. A note from your resourceful and enterprising professor: In developing a general formula, let v be the number of meters the track is to be above the ground and h the number of meters horizontally from the high point. See the next page for the diagram.
Wile E. Coyote
Genius Extraordinaire! Trey Cox and Scott Adamson ©2000
3
The vertical timbers are to be spaced every 2 meters, starting at the base of the mountain (x = 0) and ending where the track goes below the ground. The horizontal timbers are to be spaced every 3 meters.
Don’t forget that there has to be a front and backside to the roller coaster (or it would just fall over!).
At each intersection of horizontal and vertical timber, there is a 1 meter timber tie between the two sets of coinciding supporting timbers.
Timber supports will cost $3.00 a meter.
Since the ACME kit comes with the steel rails and cart but not the timber supports, please provide me with the following information:
So I can try to understand the mathematics behind your calculations give me a general formula for the sinusoidal roller coaster track.
What is the length of the vertical timber I need at the high point? What is the length of the horizontal timber I need that will be 24 meters above the ground?
Where will the track first go below ground? Where will it first come back out from below ground level? What are the lengths of each horizontal and vertical timber support?
What is total length of all the timber supports so that I will know how much to purchase?
How much money will it cost me to purchase the timber supports? Finally, with my storied history of accidents, I am a little concerned about heights. Can you give me an estimate of how steep the roller coaster will be at its steepest point?
It has been so long since I have had the delicacy of Road Runner Delight, I would appreciate your response by _________________. This will give me enough time so I can make preparations for the best meal I have had in years and invite the whole den over!
I anxiously await your reply…, Wile E. Coyote (Carnivorous Vulgaris)
P.S. A note from your resourceful and enterprising professor: In developing a general formula, let v be the number of meters the track is to be above the ground and h the number of meters horizontally from the high point. See the next page for the diagram.
