HEIGHT OF A ZERO GRAVITY PARABOLIC FLIGHT MATH

HEIGHT OF A ZERO GRAVITY PARABOLIC FLIGHT MATH 1010 Emmaline Tidd Andi Westover Rachel Dearth

PART ONE… Write 3 by 3 system of equations for a, b &c. Equation 1: 23645= a(2)^2+b(2)+c 23645=4 a+2 b+c Equation 2: 32015=a(20)^2+b(20)+c 32015=400 a+20 b+c Equation 3: 33715=a(40)^2+b(40)+c 33715=1600 a+40 b+c

PART TWO… Solve the system. Using equation 1 & 2 Eliminate A: -100(23645=4 a+2 b+c) (32015=400 a+20 b +c) -2364500=-400 a-200 b-100 c 32015=400 a+20 b+c Equation a) -2, 332, 485=-180 b-99 c

PART TWO CONTINUED… Eliminate A with another system of equations. Use equation 2 & 3 System: -4(32015= 400 a+20 b+c) (33715= 1600 a+40 b+c) -128060=-1600 a-80 b-4 c 33715= 1600 a+40 b+c Equation b) -94345= -40 b-3 c

PART TWO CONTINUED … Set up the two new equations: a and b Choose another variable to eliminate, we chose ©. System: -2, 332, 485=-180 b– 99 c -33 (-94345= -40 b-3 c) -2, 332, 485=-180 b-99 c 3, 113, 385=-1320 b+99 c 780, 900=1, 140 b 780, 900/1, 140=68. 5 b=685

PART TWO CONTINUED … Plug answer for b into either equations a or b. Answer: b=685 Plugged into equation b: -94345=40(685)-3 c: -94345=-27400 -3 c -66945=-3 c C=22315

PART TWO CONTINUED … Plug in values (b) and (c) into an original equation. We chose to plug it into equation 3: 33715=1600 a+40(685)+22, 315 33715=1600 a+49715 -16000=1600 a -10=a

PART THREE… Use the solutions from part two to form a quadratic model of data. a= -10, b=685, c=22, 315 H(t)=a^2+bt+c (plug in values) and solve: H(t)= -10^2+685+22, 315

PART THREE CONTINUED… H(t)=-10^2+685+22315 -22315= -10(t^2 -68. 5) complete the square: (68. 5/2 =34. 5) (34. 5^2= 1173. 063) -22315= -10(t^2 -68. 5+1173. 063) times 1173. 063 by the -10 = -11730. 63 and add to the other side: -22315+ -11730. 63= 34048. 63 H(t)=34048. 63=-10(t^2 -68. 5 t=34048. 63) Factor and simplify H(t)= -10(t^2 -34. 5)^2 +34048. 63

PART FOUR… Define parts. H(t)= -10(t-34. 25)^2 + 34045. 6 Find (h, k) H= -34. 25, K=34045. 6 (-34. 25, 34045. 6) Maximum is at 34045. 6

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CRITICAL THINKING From the group’s previous knowledge and experiences, we all agreed that our opinion that math can be applied to any aspect of life has not changed. This project has only presented another way that math can be used. For a career in aviation or any occupation, or to keep our luxurious lifestyles and to continue to improve, for example with technology and learning/research projects. We need math to maintain and improve our ways of life.