Question

A 75 kg mass is shot from cannon straight up with an initial velocity of 20m/s off a bridge that is 150 meters above the ground. If air resistance is given by 5v determine the velocity of the mass when it hits the ground.

Answer 1

A 75kg So let 2(t) be position of the masfemctiun ism melerts mass is Shot from cannon straight up with an initial velocity of zomis off a bridge that is 150 meters above the ground. It air resistence is given by sv delermine the velocity of the mass when it hits La resta planta 2100 sol m = 75 kg the ground. VO) = 20 mis 20) = 150m air resistence 5V 1 Kodiq Tog radairosdret som we know that F=ma F=-mg Exir resistence of 3233343 real olor E-mg - 5vp aan -mg-5v=ma ma +5v=-mg we Com write this as differential homo the non genaus equation. a- dv dz dt va dtsh da Toode men +5dx -- maz dy sharo marido a فعلے - та alrigledno in let g = 10 m/secz i pala sa kalangan di teisel 75 +5 dx belirten Barcelona -75 (10) dt dz dt² glob groot +8 da d²x dt 7 dt 75

d²x + with da = -10 على homo geneas differential equation dx + =0 dt2 15 at dx 2 da de=03 dx dt -DX (D?+ 75 D 7X=0 DCD+ 15 )=0 D=0; D = D = -1/ forvi! The Complementary solution XcZ) = 6 + cze -t

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20= -1 -150 IS 15 ته قرار 19 20+150 =-=- rito Dionis Hrvo] sigrizao zrkaqesotody progai pavo to bivibrat color copia ni C2 = 170x15' =1;-2550 not so grind , zrin aripiorary to opport gros m od 41+(2,18 1501 bioreal2013 bado 2013 sborno corrente.) - 2550 +4=150.29ry colexia feroosbo CoN 2014] afshing 296 2 150+2550,= 2700 vision and as Lion 2005 srt FDD98 21907205! rent X(t) = 2700-2550 e 5 -15oC) stresemolo Doctorispor X(t) = 2700 1 sot: meters DAT ordenad . t DET -t 2550. e T5 Va dxst) -€ 170 < Velocity (2700, -2550is -150.6) at stoot ho 1402 xposed. Aga muils trigia V= +2556 150212 m2 111.32 anyos bandi? Srit fogz -150.92 meler/sec 15 =171 -t 170 € 15 Hoaine 00 TI TO A BIT ODD 1901 Kondom i sad