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AEM2012_Exam1_Spring2008_Soln - AEM 2012 — Examination#1...

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Unformatted text preview: AEM 2012 — Examination #1 — Spring 2008 Problem #1: A cannon is trying to hit a target on the top of a 100m tall building at a distance of 10km. The angle 9 that the cannon barrel makes with the horizontal is n/6. Neglecting air resistance, find the speed V0 that the shell must leave the cannon at so that it will hit the target. " I A r 1+) = 15ml +Jlklé [L0320 ]“ ,{ 1 00m 9°“ V WWW) ”K“ M 3- .. D: A A A PB I L1 XE: N9; —3 -mcsa' = Ctxi+43§ -mfi w) a: = “x 1“ +3; l<€nzmcH ‘5 i v H db . “ " i z 0 ‘} I 7L kt) = (V031 5413 TWA =(\Ia)gt + Q ‘7 1. = _ LL}: _ 4: + v9 1: j ’3. 3Le3=-5£+ M)? #3 2.5) a): lax—HA} (MM-knits: Cflb~ banfi‘tnwd's, XIOX-JD av (i=0 K taun=o=x> D=o 1 5(10): (V°)X‘ Va (”$9 ’ (3L0):- Kvol)‘3= Vosme HH’ TMayL Cec‘oh'xk‘vrsj ; “—— loo \00m 1. 5'9 (‘1 mtg) = was: =u9;n::s = -%;5i>; 4‘ V0435; 2 65m; 1',“ Ln gut/fl = V0 Lose {:f = tokm, V0) 54 (1) => Va " “moo £4 case (3’3 P‘VS ‘31 ""i" “3 i 2. = age: 4. «w W) a = am «w fugue .. V1. i N {:4 a [mono Jame my] WI; __. 3%.Ol SewaA \/.> = “7mm 3’- 33““ 59- "/5 3‘1-Ol2ec (0580" __.____.__— AEM 2012 — Examination #1 — Spring 2008 Problem #2: A particle moves along the spiral shown where b is a constant. Determine the magnitude of the velocity of the particle in terms of b, 6, and 0. $33 acmnman, x: r er + ré é“a , 1 3 .1. b .‘L ‘ \/V‘+~qe U Mud» r in 4mm: 01! E3639. Us: mama d-fiwnm‘m: ¢§ ’ 1. . ~£relztnj =4> ref-\— r9 =0 =§> @914. 2r99=0 Mr. ’? ‘i‘ producir) (Chain (HIKE, rule, . -Z~rsé ’ ' . Y‘ =‘ 1.. - _ zre =4 "’ 31.... ~19— : ~ gin—9 (13 9 e j 9 a” 9" r:‘°/91 mwa to.) {n40 m 1.01 K... \ Vt we» We - 4 “L : ______.._\, = W- '— 9‘” 9“ a“ ‘1 J- 4: 6'", qs . + v ‘79 cpl; Q n y 1| c" ——.. a .1: + <17 f' AEM 2012 ~ Examination #1 — Spring 2008 Problem #3: The mass of triangular shape A is mA = 25 kg, the mass ofblock B is m,» = 20 kg. The surfaces between mass A and mass g l B, and mass A and in the incline are smooth with zero friction. The system is released from rest. If 9 = 45°, compute the vector representations of the accelerations of masses 1:, Incline AandB. Kinemwlics: 9A?- an (“59“ +9493) ’— 0. 3 I" . _ NB/A 084‘ J C13" Ctn" QB/A ‘3 (‘3 mm ya: NA'L~$§n91+wSG8) N” ‘6 2 F1 ‘3’ ”A9053 - N3 "W‘A‘g = moan 5M9 (2-) Ugh: NA) a“) N8 F (Q23)! B: Y X -.- O = O QQS'MQ +CL3/A :0 A 0 Beta.“ U“): (Qua; :. 0.“ 0:59 1 + an Sinfig + (lg/A ‘i 0“ ’ Lag):— CLASCAQ (a) ‘l %olve m am): (oJoaMora emailed) ...
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