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ATHS&IAT G12 ES Term I Math Project This project covers the application of the early topics in calculus ( Differentiation and its applications ) G12 ES_MATH Project 2 Grade 12 Mathematics Project Term 1 (2012/13) Date due: Nov 14 GRADE: 12 ES SECTION: Students’ Name: Differentiation Project In this project you will work with one of the most important processes of calculus Differentiation. You will apply the rules you have learnt to find answers of real life problems that have faced the aircraft engineers during a full Airbus journey. Derivatives Basic Rules Implicit Diff & Related Rates Applications of Differentiation G12 ES_MATH Project 3 G12 ES_MATH Project 4 Internet Search Introducing Airbus A 380, Collect the following information about that aircraft. History about Airbus A380. Airbus A380 characteristics. How long it takes an A 380 to takeoff. What is the takeoff velocity? What is the takeoff distance, i.e. the runway length that will be crossed before it takes off? Waiting at the airport The average number of airplanes waiting in a modern airport to take off can b e m o d e l e d b y t h e f u n c t i o n 𝑤(𝑥) = 𝑥2 2(1−𝑥) where 𝑥 is a quantity between 0 and 1 known as the traffic intensity. Find the rate of change of the number of a i r p l a n e s w a i t i n g w i t h r e s p e c t t o t h e t r a f f i c i n t e n s i t y w h e n 𝑥 = 0.1 a n d 𝑥 = 0.7 G12 ES_MATH Project 5 Taking-off Distance and Time Suppose that the distance an Airbus travels along a runway before tak ing off is given by 10 𝐷 (𝑡 ) = ( ) 𝑡 2 9 meter measured from the starting point, and 𝑡 is measured in seconds from the time the brakes are released. The aircraft will become airborne when its speed reaches 72 meters per second. How long will it take to become airborne, and what distance will it travel in that time? G12 ES_MATH Project 6 Speed of an airplane by Radar If this airplane was flying on a flight path that would take it directly over a radar station, as shown in figure below. If “s” was decreasing at a rate of 400 miles per hour when “s=10miles” what is the speed of the plane? Aircraft Glide Path Now the Airbus starts descent from an altitude of 1 mile, 4 miles west of the runway. F i n d t h e 𝑎, 𝑏, 𝑐 a n d 𝑑 i n t h e f u n c t i o n [−4,0] 𝑓(𝑥) = 𝑎𝑥 3 + 𝑏𝑥 2 + 𝑐𝑥 + 𝑑 on the interval that describes a smooth glide path for the landing. The function you founded models the glide path of the plane. When would the plane be descending at the greatest rate? G12 ES_MATH Project 7 Shockwave Read about Doppler effect of moving objects. You may Use these link to know more about Doppler effect http://goo.gl/cwYeo or http://goo.gl/E9Svc Now if the frequency F of an airbus landing on runway heard by a stationary observer on 𝐹 = 𝑣+𝑣𝐿 𝑓 𝑣+𝑣𝑠 𝑠 where F is frequency perceived by the o b s e r v e r , 𝑓𝑠 i s t h e f r e q u e n c y o f t h e s o u r c e , 𝑣 i s t h e v e l o c i t y o f t h e w a v e s , 𝑣𝐿 i s t h e v e l o c i t y o f t h e l i s t e n e r a n d 𝑣𝑠 t h e v e l o c i t y o f t h e s o u r c e . F i n d a n e q u a t i o n o f t h e 𝐹 i n t e r m o f 𝑣𝑠 . T h e n f i n d t h e r a t e o f c h a n g e o f 𝐹 w i t h r e s p e c t t o 𝑣𝑠 , I n t w o c a s e s o n c e w h e n a i r b u s i s a p p r o a c h i n g a t v e l o c i t y of 200km/hr, and the other whe n its moving away at a velocity 200km/hr Presentation Prepare a presentation including a wiki to show your findings, include videos, your own work, and other related information. Produce a QR code for your wiki. G12 ES_MATH Project 8 Projects Rubric Guidelines Criteria 4 Completeness of Tasks 20% Presentation and Integration of Technology 70% Creativity& enrichment 10% Points 3 2 1 Tasks are totally completed and correct. (100%) Tasks are partially completed, OR Partially wrong.(75%) Tasks are partially completed, AND Partially wrong (50%). Tasks are Attempted (25% or less) ____ Students used one mean of technology. The tool used helped the student and was useful to support his project. Moreover, the student was able to explain the work he/she submitted confidently and fluently; he/she was able to answer all of colleagues and instructor’s questions Student used a mean of technology but it was not that supportive to the topic. In addition, student was able to explain the work he/she submitted confidently and fluently and he/she reflected an understanding of his/her works. The student was able to answer most of colleagues and instructor’s questions. Student was able to explain the work he/she submitted. Student reflected a shallow understanding of his/her work; she was able to answer some of colleagues and instructor’s questions, Student use of technology was primitive and way below the level of other IAT students. Student was unable to explain the work he/she submitted. Student reflected no understanding of his/her work; he/she was unable to answer any of colleagues and instructor’s questions. ____ Student had an outstanding addition in all aspects of his/her project. Student had an outstanding addition in some aspects of his/her project. Student had an outstanding addition in very few aspects of his/her project. Student had an outstanding addition in no ____ aspects of his/her project. This rubric is out of 100 percentage orientation. To make the mark out of 20 (Student’s Mark/10*2) Total---> ____