Human Cannonball Key

The Human Gannonball Must Live to Flv Asain (her life is in vour handslThe Human Cannonball is the highlight of the Cartesian Circus. When the Human Cannonballis fired from the cannon, she should fly through a Ring of Fire and land in a net on the oppositeside of the Circus arena. The Ring of Fire is located at the center of the circular arena andsuspended so that its center is 40 feet above the ground. The cannon stands on a rollingplatform that can be raised up to 22 feet. The top of the cannon is 4 feet above the cannonplatform, and the angle of the barrel cannot be altered.Initially, the cannon platform, Ring of Fire and landing net are lined up along the 1S0-footdiameter of the arena, with the cannon platform on the ground at the edge of the arena, andthe landing net 5 feet above the ground at the opposite side of the arena. Using this setup, theHuman Cannonball will be hurled along a parabolic trajectory (path) described by the func{ionA(x)=-O.Ottx2 +0.9x+4,where ft(r) isfireheightof theHumanCannonball abovetheground and x is the distance from the cannon platfonn along the arena's diameter.Unfortunately, this trajectory will not send the Human Cannonball through the Ring of Fire, andthe audience will demand a refund. You are the stage hand in charge of positioning theplatform and landing net so that the circus will not go bankrupt and the Human Cannonball willlive to fly again.1) Draw a sketch to represent the initial problem situation. Show the cannon, the Ring of Fire,the landing net, and the path pJ the Human Cannonball.\I,Je*t50I

2) Let the cannon platform be at the origin. Give the coordinates of the following in the initialproblem situation:COORDINATESCannon PlatformRing of Fireo?r4Ll oNetIQ 5xv3)Assuming the cannon's platform is at the origin, use a graphing utility to graph the initialparaboliCtrajectory of the Human Cannonball, as well as the points where the Ring of Fireand the net ire located. Paste a copy of your labeled graph in the space below (be sure toindicate your scale along each axis).'(7.?it) GnL-as-to,or.'[*lo,qx+q . loI cb'nr\o nlott\'6tett1lnF p,u+t", (t5otdtr NAY

!+lthe equation for the path of the Human Cannonball to shift the cannon platformhorizontally and/or vertically to try to get the Human Cannonball to pass through the centerof the Ring of Fire. Graph your modified equation to see how well the modified equationworks. Repeat as many times as necessary to get the Human Cannonball through theof the Ring of Fire. What is your final modified equation? Paste a labeled copy ofyour graph in the space below (again- be sure to indicate your scale along each axis)..rl-Cm{d.nCr,tgi:,-------*--Modifyg:\u\ centert 5l* OF1;lil?F'---j ,(?4 tl''lo +5 - LJ CI, qoQOEZ -,34, 01O1Ot \(Uoqc4 D{:-, l>'qc'rcn t) qtr; {+. )r i M VL.', acty qof,'/uni\ S.f C)-c l-coord;tn&fe:;nn&{--e :t.lO - 22-,LlOqDe l: tV,57O?0?FZV F3ZooFl fneceCxi\frttAr{RegnephItlat,hF5v ' FE?Enatrl€hi++ u,p l7,Sqo?g? Ltl dSti hfx] = - O,ot\Z'+O,q/+Ll,:f t:uo"tto/\To?pd-r lv,\1 01tr(r{o,f)F,lftll{-+l,tufyldt4 pto+6.^n -io $1,'a r,1h* H'oQo?Zgvrr f5 o n& up l+,510?o? I rril-55) So ... where should you place the cannon platform so that the Human Cannonball will flythrough the Ring of Fire?6) More importantly, since the landing net is S-feet high, where should you place the net sothat the Human Cannonball will live to fly again? flEao ;r*ergcl J"t"o. huY'non I-cbn no,t\wo rtt € r'rr,tn} . o*+J^-0\o c?- \4"o nLV o*'g,Atoo,rdi rno kg Cr fe,zL++*t, =J,