“The great calculus II Conundrum” Background: It is the year 2030.The Characters
ID: 2870460 • Letter: #
Question
“The great calculus II Conundrum”
Background:
It is the year 2030.The Characters In this murder mystery were classmates at the United States and graduated in the year 2000. All were advanced placed Calculus II students the first semester of their freshman year. They retired as Lt Colonels and started a small business named “ITSI” (Innovative Techniques for solving Integrals).The business folded after five years and the four partners went their separate ways (although they kept in contact with each other as all alumni do). The four characters are: Lt Col Taylor, Lt Col Riemann, Lt Col Trapezoid, and Lt Col Euler. As all four prepare to gather to meet tonight at Lt Col’s Euler’s cabin outside of Colorado Springs, we find that Lt Col Euler has been murdered –the other three Lt Cols are the primary suspects.
Clue 6: We know that two of the Lt Cols had a motive. We also know the time of the murder. If we know where the suspects were at the time of the murder, our mystery would be solved! All three suspects left their homes at approximately 1900. Who committed the murder?
a.Lt Col Riemann must travel a long, winding road to reach Lt Col Euler’s home. The shape of the road can be approximated by the function y=sin(x) and the straight line distance between Lt Col Riemann’s home and Lt Col Euler’s home 40 miles (the distance actually travelled is the length of the road).Lt Col Riemann drives at an average speed of 30 miles per hour.
b.Lt Col Taylor is an avid hiker and lives a very short distance from Lt Col Euler’s home. He knows the way well. Although the straight line distance between Lt Col Taylor’s and Lt Col Riemann’s home is only 2 miles, a large hill stands between the two homes and Lt Col Taylor must hike over the hill. The trail can be approximated by y=4-(2x-2). Lt Col Taylor hikes at an average speed of 8.4 miles per hour.
c.Lt Col Trapezoid was on the jump team as a cadet and still enjoys jumping. Since the jump team happens to be practicing that evening, she decides to jump in to the meeting at Lt Col Euler’s. Since Lt Col Trapezoid lives in Glen Eagle, it only takes her 15 minutes to reach the flight line and the plane is ready for take-off when she arrives. She boards the plane and is just above Lt Col Euler’ home 20 minutes later. She jumps from 400 ft and from the time of her jump until the time she lands, her average velocity was 30 ft/sec.
Then do the following cadet response:
Cadet response is in the following form:
My solution…………….did it in the……… with the…… at about………….and put the body in the………………………….
Explanation / Answer
The first person to reach the home will be going to murder the Lt. Euler
The time taken by Lt Col Rienmann
The distance is travelled by y=sin(x) path the distance between two points is 40 miles, assuming it is radius R, then sin(x) path will move the distance equal to pi*r
Hence the distance on y=sinx path from Rienmann to Euler is 40*pi miles
Hence time taken will be equal to 40*pi/30 = 4.186 hours
The time taken by Taylor can be evaluated by using the speed 8.4 km/hr, hence total distance travelled will be equal to
16 and speed 8.45 miles/hr
Hence time taken is 16/8.45 = 1.893 hours
The time taken by Lt Col trapezoid
15 + 20 + (400ft/30ft)/60
=> 35.22
Hence according to the solution
My solution is Col Trapezoid did it in the 35 minutes with the time 19:35 and put the body in the grave
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.