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BOAR D PROB LEMS TRANSPOR TRANSPORT TATION ENGINEERING Submitted by: Jan Roald B. Triumfante
em: 1.Probl I ti sest i mat edt hatbet weent hehour sofnoonand7: 00P. M.t he speedofahi ghwayt r afficflowi ngpastt hei nt er sec t i onofEDSAandOr t i gas Av enuei sappr oxi mat el y 3 2 S=t –9t +15t+45kph Wher e“ t ”i st henumberofhour spas tnoon
Requi r ed: atwhatt i mebet weennoonand7: 00P. M.i st het r afficmovi ngt he f as t e s t ? 3 2 Gi ven:S=t –9t +15t+45kph
For mul a:d/dx( un)=nun-1 3 2 S=t -9t +15t+45
Sol ut i on:
Appl yt hef or mul ad/dx( un) =nun-1 2 dS/dt=3t –18t+15=0
00 P. M. Ther ef or et het r afficmov esf as t es ti sat1: em: 2.Probl Thepeakhourf act orf orat r afficdur i ngrushhouri sequalt o0. 60 wi t hahi ghes t5mi nv ol umeof250v ehi cl est hespacemeanspeedoft het r affic i s90kph Requi r ed: Comput et heflow oft r affici nve hi cl es /hour Gi ven:PHF=0. 60;t r afficv ol ume=250vehi cl es ;t i me=5mi n For mul a:PHF=flow oft r affic/t r affic( 60/5) Sol ut i on: PHF=flow oft r affic/t r affic( 60/5) 0. 60=flow oft r affic/250( 60/5) q=1800vehi cl es/hour obl em: 3.Pr At2: 00P. M.anai r pl anet akesoffat340mphonanai r cr af tcar r i er . Theai r cr af tcar r i ermov esduesout hat25kphi nt hesamedi r ect i onast he pl ane.At4: 05P. M.t hecommuni cat i onr angei nmi l esbet weent hepl aneand t hec ar r i e rwasl o s t . Requi r ed: Det er mi net hecommuni cat i onr angei nmi l esbet wee nt hepl aneand t hec ar r i e r Gi ven:t i me=af t er2: 00P. M. ;at4: 05P. M. ,t=2hr sand5mi n=2+5/60
Sol uti on : =340t–25t=315t x 25mi l es x=315( 2+5/60)=656. obl em: 4.Pr Acarwast r av el l i ngataspeedof50mph.Thedr i v ersaw ar oadbl oc k 80m aheadandst eppedont hebrakecausi ngt hecart odece l er at euni f orml yat 2 10m/s. Requi r ed: Fi ndt hedi st ancef r om t her oadbl ockt ot hepoi ntwher et hecar st opped.Assumeper cept i onr eact i ont i me2sec. Formul a:S1 =vot 1 2 2 2 v =v +2aS o Gi ven:d=80m;vo =50mi /hr=22. 36m/s;S1 =22. 36( 2)=44. 72m 2 2 2 Sol ut i on : =vo v +2aS 02 =22. 362 +2( 10) S2 S2 =25m 28m d=80–S1 –S2 =80–44. 72–25=10. em: 5.Probl I ti sest i mat edt hatbet weent hehour sofnoonand7: 00P. M.t he speedofahi ghwayt r afficflowi ngpastt hei nt er sec t i onofEDSAandOr t i gas Av enuei sappr oxi mat el y 3 2 S=t –9t +15t+45kph Wher e“ t ”i st henumberofhour spas tnoon
Requi r ed: Atwhatt i mebet wee nnoonand7: 00P. M.i st het r afficmovi ngt he s l o we s t ? 3 2 Gi ven:S=t –9t +15t+45kph
For mul a:d/dx( un)=nun-1 Sol ut i on:
3 2 S=t -9t +15t+45
Appl yt hef or mul ad/dx( un) =nun-1 2 dS/dt=3t –18t+15=0
00P. M. Ther ef or et het r afficmov essl owes ti sat5: em: 6.Probl I ti sest i mat edt hatbet weent hehour sofnoonand7: 00P. M.t he speedofahi ghwayt r afficflowi ngpastt hei nt er sec t i onofEDSAandOr t i gas Av enuei sappr oxi mat el y
3 2 S=t –9t +15t+45kph
Wher e“ t ”i st henumberofhour spas tnoon
Requi r ed : ati Wh st hesl owes tspeedi ti smovi ngatt hi st i me? 3 2 Gi ven:S=t –9t +15t+45kph
For mul a:d/dx( un)=nun-1 Sol ut i on:
3 2 S=t -9t +15t+45
Appl yt hef or mul ad/dx( un) =nun-1 2 dS/dt=3t –18t+15=0
S=20kph em: 7.Probl Thepeakhourf act orf orat r afficdur i ngrushhouri sequalt o0. 60 wi t hahi ghes t5mi nv ol umeof250v ehi cl est hespacemeanspeedoft het r affic i s90kph Requi r ed: Comput et hedensi t yoft r affici nvehi cl es/km Gi ven: PHF=0. 60;t r afficv ol ume=250ve hi cl es ;t i me=5mi n;us =90 Formul a:q=usK Sol ut i on: q=usK 1800=90K K=20 vehi cl es/hour em: 8.Probl Thepeakhourf act orf orat r afficdur i ngrushhouri sequalt o0. 60 wi t hahi ghes t5mi nv ol umeof250v ehi cl est hespacemeanspeedoft het r affic i s90kph Requi r ed: Comput et hedensi t yoft r affici nvehi cl es/km Gi ven: PHF=0. 60;t r afficv ol ume=250ve hi cl es ;t i me=5mi n;us =90 Formul a:spaci ng=1000/K Sol ut i on: spaci ng=1000/20 Spaci ng=50m centert ocent er em: 9.Probl Thepeakhourf act orf orat r afficdur i ngrushhouri sequalt o0. 60 wi t hahi ghes t10mi nv ol umeof500v ehi cl est hespacemeanspeedoft het r affic i s100kph Requi r ed: Comput et heflow oft r affici nve hi cl es /hour
Gi ven:PHF=0. 60;t r afficv ol ume=500ve hi cl es ;t i me=10mi n Formul a:PHF=flowoft r affic/t r affic( 60/10) Sol ut i on: PHF=flow oft r affic/t r affic( 60/10) 0. 60=flow oft r affic/500( 60/10) cl es/hr q=1800vehi Probl em: 10. Thepeakhourf act orf orat r afficdur i ngrushhouri sequalt o0. 60 wi t hahi ghes t10mi nv ol umeof500v ehi cl est hespacemeanspeedoft het r affic i s100kph Requi r ed: Comput et heflow oft r affici nve hi cl es /hour Gi ven:PHF=0. 60;t r afficv ol ume=500ve hi cl es ;t i me=10mi n;us =100 For mul a:q=usK Sol ut i on:
