Question

2/94 An experimental fireworks shell is launched verti- cally from point A with an initial velocity of magni- tude u-100 ft/sec. In addition to the acceleration due to gravity, an internal thrusting mechanism causes a constant acceleration component of 2g in the 60" direction shown for the first 2 seconds of Aight, after which the thruster ceases to function. Determine the maximum height h achieved, the total flight time, the net horizontal displacement from point A, and plot the entire trajectory. Neglect any acceleration due to aerodynamics. 26 60 Problem 2/94

Answer 1

29 g-32-2 fte Vo- l00 ft 18e e>60 t. = 39ec 60 total accelenation X-dinechon Ve 1m ax& in y-dinection ay Fan Jinst two 9econd (t) ax= ax- 29×ミ→ ae-g Sti3- L 4y 9(-1) Adtesn tR 0n オンス/ ax =0 4 ay-9 y=dy d犬 y dt sinee elocity) Sat Righeat point t= te &valocity - \ -g dt is zeno W te キJ8-4 33](-206 O-VO=3R. fes-x-(ta-) te- 3.464+ l00 32.2 1.4641-t8+2 -100 32.2 to reach Rigkest boint な= 6-5697 Hime taken Sec Now is velocity dy7g 963-1)dt dt 100+ 47-1441 - Vo 3R.2 (-)) (2-0)) V こ147.1441 St/aec

From VURA39S s-1)4S ve V.=v3 +2(5-1)9 isReigR at t3 147-144-l00 AS247.1441 -1)X3-2 SNow fan V a=-9, S= AH-A o147-1A4143 (-33.2) (H-A2 147.1441 M-A2 H-336.R0IS +RA7 AA R3R-2 H =583.3456 CHig Regt boint in-dinecthion) ReigRt -583.3 .3456 maximum Fnom Rene S-R tis gaou m ig Rest boind time faken by ball to seacR 583-3456=0+ 5 RX683-3456 > t= 6.03 gec 3R-2 time digRT total tf= 6.5697+ 6.02 ts= 1R.589 sec An Sy=S, t Sky X-di'nechionor t-o to t= Ste Net Bosizontal disblacement S2 is displa ce ment in is displacement in -dinec tion on t=2 tb t=5 Sx=OXR+ + gx2x (R.589-2) x (12. 503-2) SRene uzo len to ax SyMOT SRORX2 +RX3R.2x (lo S89) +o SeT46.335 St Since utat So Va-39 dan t 740 0z

583.34S6 at te2 2A7-1441 64. A 746 3352

Editor D:\matlab programs\sheet3\Untitled.m x Untitled.m fun.m X tdma.m + clc: tl -linspace (0,2,100); t2 linspace (2,12.59, 100); xl- (32.2/2) tl.^2; x2 64.4+2*32.2* (t2-2) ; yl -100 tl+11.786*tl.^2; y2-247.1441l+147.1441* (t2-2) -16.1* (t2-2).^2; 4 plot (xl,yl,x2, y2) CO 2 3

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