Engineering Mechanics (Projectile Motion)
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Engineering Mechanics Exercise on Projectile Motion (Unit-III) 1 A projectile is fired with velocity 620 m/s at an angle of 40 with horizontal ground. Find the range, time of flight, maximum height attained by projectile and the velocity just before striking the ground. 2 A projectile is fired from a edge of 150 m cliff with an initial velocity of 180 m/s at an angle of 30 degree with horizontal. Neglecting air resistance determines (a) Horizontal distance from the gun to the point where projectile strikes ground (b) the greatest elevation above the ground reached by the projectile. 3 A projectile is fired with an initial velocity of 244 m/s at target B located 610 m above the gun A and horizontal distance of 3658 m. determine value of firing angle 4 A tennis player serves the ball at a height h with an initial velocity of 40 m/s at an angle of 4° with the horizontal. Knowing that the ball clears the 0.914 m net by 152 mm, determine (a) the height h, (b) the distance d from the net to where the ball will land. 5 A golfer hits a ball with an initial velocity of magnitude v 0 at an angle α with the horizontal. Knowing that the ball must clear the tops of two trees and land as close as possible to the flag, determine v 0 and the distance d when the golfer uses (a) a six-iron with α = 31°, (b) a five-iron with α = 27°. 6 A ski jumper starts with a horizontal take-off velocity of 25 m/s and lands on a straight landing hill inclined at 30o. Determine (a) the time between take-off and landing, (b) the length d of the jump. 7 A bullet is fired from horizontal distance of 44m measured from bottom of a 12 m high vertical pole. Calculate velocity of projection such that bullet can just clear the upper end of the pole 8 A shot is fired at an elevation of 60 degree with velocity of 60 m/s. State the position of the shot at 2 sec after firing. What will be velocity at that instant? 9 A homeowner uses a snow blower to clear his driveway. Knowing that the snow is discharged at an average angle of 40° with the horizontal, determine the initial speed v0 of the snow.
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Beer Dynamics
Transcript of Engineering Mechanics (Projectile Motion)
Engineering Mechanics Exercise on Projectile Motion (Unit-III) 1Aprojectileisfiredwithvelocity620m/satanangleof40withhorizontalground.Find therange,timeofflight, maximum height attained by projectile and the velocity just before striking the ground.2A projectile is fired from a edge of 150 m cliff with an initial velocity of 180 m/s at an angle of 30degreewithhorizontal.Neglectingair resistancedetermines(a)Horizontaldistance fromtheguntothepointwhereprojectile strikesground(b)thegreatestelevationabove the ground reached by the projectile. 3Aprojectileisfiredwithaninitialvelocityof 244m/sattargetBlocated610mabovethe gunAandhorizontaldistanceof3658m. determine value of firing angle 4Atennisplayerservestheballataheighth with an initial velocity of 40 m/s at an angle of 4withthehorizontal.Knowingthattheball clearsthe0.914mnetby152mm,determine (a) the height h, (b) the distance d from the net to where the ball will land. 5Agolferhitsaballwithaninitialvelocityof magnitudev0at an angle with thehorizontal. Knowingthattheballmustclearthetopsof twotreesandlandascloseaspossibletothe flag,determinev0andthedistancedwhenthe golferuses(a)asix-ironwith=31,(b)a five-iron with = 27. 6Askijumperstartswithahorizontaltake-off velocity of 25 m/s and lands on a straight landing hillinclinedat30o.Determine(a)thetime betweentake-offandlanding,(b)thelengthdof the jump. 7 A bullet is fired from horizontal distance of 44m measured from bottom of a 12 m high vertical pole. Calculate velocity of projection such that bullet can just clear the upper end of the pole 8 A shot is fired at an elevation of 60 degree with velocity of 60 m/s. State the position of the shot at 2 sec after firing. What will be velocity at that instant? 9Ahomeownerusesasnowblowertoclearhis driveway. Knowing that the snow is discharged atanaverageangleof40withthehorizontal, determine the initial speed v0 of the snow. 10A golfer aims his shot to clear the top of a tree by adistancehatthepeakofthetrajectoryandto miss the pond on the opposite side. Knowing that the magnitude of v0 is 30 m/s, determine the range of values of h which must be avoided. 11AhandballplayerthrowsaballfromAwitha horizontalvelocityv0.Knowingthatd=15ft, determine(a)thevalueofv0forwhichtheball will strike the corner C, (b) the range of values of v0forwhichtheballwillstrikethecornerregion BCD. 12Ahelicopterisflyingwithaconstanthorizontal velocityof90mi/h(144.2kmph)andisdirectly abovepointAwhenaloosepartbeginstofall. The part lands 6.5 s later at point B on an inclined surface.Determine(a)thedistancedbetween points A and B, (b) the initial height h. 14Abasketballplayershootswhensheis5m fromthebackboard.Knowingthattheballhas an initial velocity v0 at an angle of 30 with the horizontal,determinethevalueofv0whendis equal to (a) 228 mm, (b) 430 mm. 15A ball is projected from point A with a velocity v0 whichisperpendiculartotheinclineshown. KnowingthattheballstrikestheinclineatB, determinetheinitialspeedv0intermsofthe range R and . 16Anoutfielderthrowsaballwithaninitial velocity of magnitude v0 at an angle of 10 with thehorizontaltothecatcher50maway. Knowingthattheballistoarriveataheight between0.5mand1.5m,determine(a)the range of values of v0, (b) the range of values of the maximum height h of the trajectory. 17AmodelrocketislaunchedfrompointAwith aninitialvelocityv0of86m/s.Iftherockets descentparachutedoesnotdeployandthe rocketlands104mfromA,determine(a)the anglethatv0formswiththevertical,(b)the maximumheighthreachedbytherocket,(c) the duration of the flight. 18The initial velocity v0 of a hockey puck is 170 km/h. Determine (a) the largest value (less than 45)oftheangleforwhichthepuckwill enterthenet,(b)thecorrespondingtime required for the puck to reach the net. 19AprojectileislaunchedfrompointAwithan initial velocity v0 of 120 ft/s at an angle with the vertical. Determine (a) the distance d to the farthestpointBonthehillthattheprojectile canreach,(b)thecorrespondingangle,(c) the maximum height of the projectile above the surface. 20A sack slides off the ramp, shown in Fig. with a horizontalvelocityof12m/s.Iftheheightof therampis6mfromthefloor,determinethe time needed for the sack tostrike the floor and the range R where sacks begin to pile up. 21Thechippingmachineisdesignedtoeject woodchipsatv0=25ft/sasshowninFig.If thetubeisorientedat30fromthehorizontal, determine how high, h, the chips strike the pile if at this instant they land on the pile 20 ft from the tube. 22The ball is kicked from point A with the initial velocity10m/s.Determinethemaximum heighthitreaches.AlsoDeterminetherange R,andthespeedwhentheballstrikesthe ground. 23Determinethespeedatwhichthebasketballat Amustbethrown at the angleof 30 so that it makes it to the basket at B. 24Waterissprayedatanangleof90fromthe slope at 20 m/s. Determine the range R. 25AballisthrownfromA.Ifitisrequiredto clearthewallatB,determinetheminimum magnitude of its initial velocity. 26Aprojectileisfiredwithaninitialvelocityof 150 m/s off the roof of the building. Determine the range R where it strikes the ground at B. 27The ball i s thrown off the top o f the building. If it strikes the ground at B in 3 s, determine the initialvelocityandtheinclinationangle( )A atwhichitwasthrown.Also,findthe magnitudeoftheball'svelocitywhenit strikes the ground. 28Thefiremanholdsthehoseatanangle( )= 30 with horizontal, and the water is discharged fromthehoseatAwithaspeedofvA=40 ft/s.Ifthewaterstreamstrikesthebuildingat B,determinehistwopossibledistancessfrom the building. 29A projectile is fired with a speed of v = 60 m/s atanangleof60.Asecondprojectileisthen fired with the same speed 0.5 s later. Determine theangle( )ofthesecondprojectilesothat the two projectiles collide. At what position (x, y) will this happen? 30Water is discharged from the hose with a speed of40ft/s.Determinethetwopossibleangles( )thefiremancanholdthehosesothatthe water strikes the building at B. Take s = 20 ft. 31It is observed that the time for the ball to strike thegroundatBis2.5s.Determinethespeed VA and angle A at which the ball was thrown. 32The golf ball is hit a t A with a speed o f VA = 40 m/s and directed at an angle of 30 with the horizontalasshown.Determinethedistanced where the ball strikes the slope at B. 33Ifthefootballiskickedatthe45angle, determineitsminimuminitialspeedVAso thatitpassesoverthegoalpostatC.Atwhat distancesfromthegoalpostwillthefootball strike the ground at B? 34A golf ball is struck with a velocity of 80 ft/s as shown.Determinethedistancedtowhereit will land. 35Determine the horizontal velocity VA of a tennis ball at A so that it just clears the net at B. Also, findthedistanceswheretheballstrikesthe ground.
