Pegs A and B are restricted to move in the elliptical slotsdue to the motion of the slotted link. If the link moves witha constant speed of 10 mis, determine the magnitude of thevelocity and acceleration of peg A when x = 1m.

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~2/211 A batter hits the baseball A vrith an initial velocityof Vo = 100 ft/sec direct1;)' tOVllardfielder B at an.angle or 30° to the horizontal; the initial JX>sition ofthe ball is 3 ft above ground level. Fielder B re-quires 1 see to judge where the ball should becaught and begins Inoving to that position vvithconstant speed. Beca-use of great experience, fielderB chooses his running speed so that he arrives atthe "catch position" simultaneously with the base-ball. The catch position is the field location atw-hich the ball altitude is 7 It. Deten::nine the veloc-ity of the ball relative to the fielder a.t the instantthe catch is :JD.ade.

Azrs , VA/E = 71.5i - 47.4j ft/sec

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1/119 Race car A follows path a-a while race car B followspath b-b on the unbanked track. If each car has aconstant speed limited to that corresponding to alateral (normal) acceleration of O.8g, determine thetimes iA and te for both cars to negotiate the turnas delimited by t.he line C-C ..

Ans. tA = lO.52 S, tB = 10.86 s

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12-118.

The truck travels in a circular path having a radius of 50 m ata speed of v = 4 m/s, For a short distance from s = 0, itsspeed is increased by v = (0.05s) m/s2, where s is in meters.Determine its speed and the magnitude of its accelerationwhen it has moved s = 10 m.

'V = (0.055) m/s2v = 4 m/s

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Sample Problem 2(8

A certain rocket maintains a horizontal attitude of its am during the pow-ered phase of its flight at rugh altitude. The thrust imparts a horizontal compo-nent of acceleration of 20 ft/8ec2

, and the -downward acceleration component ill

the acceleraticn due to gravity at that altitude, which is g :: 30 ft/sec2. At the in-giant represented, the velocity of the mass canter G of the rocket along the 15°direction of its trajectory is 12,000 mi/hr. For this position determine (a) the ra-dius of curvature of tbe Bight trajectory, (0) the rate at which the speed v is in-creasing, (c) the angular rate ~ of the radial line from G to the center ofcurvature 0, and (d) the vector expression for the -total acceleration a of therocket.

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2/120 The wheel and attached pulley rotate about thefixed. shaft at 0 and are driven by the belt shown.At a certain instant the velocity and acceleration ofa point A on the belt are 2 ft/sec and 6 ft/sec'l, re-spectively, both in the direction shown. Calculatethe m agrutarde of the total acceJeration of point Bon the w-heeJ for- this instant.. Observe that the lin-ear rnot.iou. of point A on the belt and the tangentialmo rton of a point on the 4-in.-radius crrcre are iden-tical and that {) and jj For the rad:ia.llines to allpoints on the wheel are the aarrre.

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2/15·} At the bottom of a loop in the vertical V··ll) plane atWI ullil.ooc of 4)0 In, Lhc d:.irplu.n~P l~ I:l hlJraon-t.n1 vclodty of 600 kln/ha llnd r:.o h or-iaorrtul accclcr-o-

t.ion. Tho l"1l.diUI: of CUlVct'.l.rO of thQ 'cop W 1200 n'J.For tho radar tl'Rcking at 0 r detennine tho recordedvalues of i: and jj for this' ristarrt

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12-181. Pin P is constrained to move along the curvedefined by the lemniscate r = (4 sin 28) fL If the angularposition of the slotted arm OA is defined by 0 = (3t312) rad,determine the magnitudes of the velocity and accelerationof the pin P when 8 = 60°,

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2/162 The robot arm is elevating and extending simulta-neously. At a given instant, (J = 300

, 9 = 10 deg/s =constant, 1= 0.5 m, l :::0.2 mis, and I = -0.3 m/s2.Compute the magnitudes of the velocity v and ac-p.p.lp.ration a of the gripped part P. In addition, I'!X-

press v and a in terms of the unit vectors i and j.

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