Soluzioni esercizi cinematica

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!#"%$&"('*),+.-0/213+546'*13/87 96+;:<>=3>"(),'?9@+A"(CBD+;E8#B?/<->'F=HG;-0/ 9 B*+.I2J6+AB*C'*BK$&J&92=3/L1M' )%J&/NE8 O QSP PRUTMVXWZY\[N]X^3_?`KaAT bcRdTMVXP We[N]Xf>g ^<aAT h@RdTMVXWei I2J&j1k=H+mlnJ&96+mE8#B?/<-0'?=(GmE 0=M=(/8"('*+8B?o$p>"H-0'*qm$p/ 1(13/%=("3/NEN+8"39&r'?B )m/<:<J6B?/@O s P RUTMVXWut sT W v R Q!P RdTMVMV3wXxeR bcP RdTMV3VMwyxeR h@P RdTMV3VMw\z [N]@{ | a n"H+A$6$&"3j1M#92=(+m$&"(/8$&"(t '?/mBD+,E8>B*/<-0'?=(G,-0/ 9}B*+~I2J6+8B? '*B $&J&92=(/ 1M' 13J&B*B*+m=("(+8'?>=M=(/8"('*+6 !#"M=H+A92=3/,BD+m:&'*1M=(+89& #+m$p>"H-0/8"H1(+ EN+AB*n1M#),$&B?'D-0#),>92=3 O soW s P RUTMV t TXz #| | :&/NE8 B*+,I2J6+89 =('F=HG oln$&"(/8$6"3'*/%B +81(-0'D131(+%->J&"(E2'*B*'?9&j+& & K \96-H & '*9 I2J&j1k=(/%j1M#"(->'? #'?/m1M' $&J6q,-#+ABD-0/ B*+8"3 ),/ BF=(/m13>),$&B*'*->>),>92=(oB*n-0/ )m$p/A 96>92=3' :&>B*B*+mE8#B?/<->'F=HGm->/8),8O P Q!RdP TMV W [ x [NT Ph@RdTMbcVXRdW TMVyYnW #a8| T 8w c M ),#9 =("3n$p>"K=("3/NEN+8"3oB +8-#-0#B?#"(+8 >'*/89&r/ -#-0/ "3"(o:&>"('?EN+A"(oJ&96+,1Mj-0/ 96:&+mE8/ BF=H+&O bcQSRdTMRUVXTMVXWZW j[[AT h6 RUTMVXW 8|8 p 3 \B?B &'D1k=H+A92=3 =0 o m'?B ),/<:<J&B*/ :<>B*BD+%E >B*/<-0'?=(GmEN+AB*8O s P R | V W t sT W v R Q P RU|2VMV w x R bpP R | V3V w xeR h@P RU|2VMV w z #| t 6 rJ6' 1M'c=("(+A=M=H+m:&' +A$&$6B?'D->+8"3oB /8$p>"H+A #'?/ 9&o'?9 E8#"(1(+&O Y ¡ RUTMV W Y ¢ RUTMV t T £ E E 'D+A),>92=3}j1M'D1k=(/89&/L'*9<¤69&'?=35$&"('*)m'?=3'*E85-H &;13/<:&:<'D1k¥U+89&/LB #I2J6+8 >'*/89&513/8$&"H+ ->'F=H+N=H+& ! !>" I2J&#1M=3/m),/A=('?E /6¦2$@#" :<0=(>"()m'*96+8"3rB '?92=(>78"H+AB*o#1(+N=M=(/6¦ lo9&#->#1(13+8"3'*/ +§E >"(}J&9¨ J&BF=(>"('?/ "3}'*9<¥d/8"()~+A #'?/ 9&8 ©ª9 I2J&j1k=(/ ->+ 1M/«'*Br:&+A=3/ +A7 78'*J&92=3'*E8/Ll5B*+ E >B*/<-0'?=(G,:<>B $&J&92=3/~+AB*B 'D1k=H+A92=3o=0 o & Y ¡ RdTMVXW ¬­ 8 p®3 x ¯ ¬ ]y^M_*` NT Y ° ¬ f>g ^<T x ±0YkY&²§³ Y&Ys# T´


Y ¡ RUTMVXW Y ¬­ i p®3 YL¯ ¬ ] f0g ^@ NT Y ° ¬ ^3_?`KT x ±>YMY&²§³ Y&s>Y T´ \B?B '*1M=(+89 =( =´ o ,13' 6+~-H & Y ¡ RU|2VXW Y ¬­ i Y.¯ ¬ ] x ±0YkY&²§³ Y&Ys# T´ rW Y ¬­cYL¯ ¬ xZ° ¬ 13>7 J&n-H & ±0YkY&²§³ Y&Ys# T´ \W Y ¬­ i[ YL¯ ¬ xZ° ¬ '*95:<0¤@9&'F=('?EN+ Y ¡ RUTMVXW Y ¬­¶µ i[ x i c®M ¸· Y ¯ ¬ µ x ] f>g ^6 AT · Y ° ¬ RU^3_?`¹T Yº jV ©ª9&¤69&»13nE8/87 B?'*/,->+ABD-0/ B*+8"3r'?B E80=3=3/ "3 $p/ 13'? #'?/ 9&n:<>4&4p/,'F=(>"H+A"( 92J6/NE§+8),>92=3oB*+ $6"3/<-0j:<J&"H+&O ½Y ¼ RdTMVyW Y ¡ RdTMV t TXWZY ¬­8 ¾µ i[ x i p®3 ¸· Y ¯ ¬ ¾µ x ] f0g2^6 NT · Y ° ¿ R ^M_*`¹T!Y §VMx ±0kY Y&§² ³ Y6s#Y TM[ Y ¼ RUTMVXWº¬­ µ Y i[ T x À c®M · YL¯ ¬ µ T Y [ ] ^3_*`\ NT · x ° ¬ R f0g2^<T x jV¨x ±0YkY&²§³ Y6s#Y TM[ '*),$@/ 9&78/,BD+m$@/21M'* >'*/89&n+8Bc=3>),$p/,=´ o 6O Y ¼ RU| V W ¬­ À x [ ° ¬ x ±>YMY&²§³ Y&s>Y TM[»We[j¬­6x ¯ ¬ x [¨° ¬ ±0YkY&²§³ Y&Ys# TM[ W ¬­ ]À x ¯ ¬ !#"(->'?q@O Y ¼ RUTMV Wº¬­¶µ Y i[ T¨xÁ p®3 · YL¯ ¬ µ T Y [ ] ^M_*`\ NT Yº · xZ° ¬ R f0g ^&T¨x jV  à +8B*->/8B*'*+8),/ '?B2E8>=M=(/8"( ¼Y w Y ¼§Y Ä Å +r1MJ6+\:<>"('?EN+A=(+K¥d/ "39&'D1(-0Xj13+A=M=H+A),>92=3X'?B2EN+AB*/8"( :&>B*B*+,E >B*/ ->'F=HG& ¶Æ >7 J&»+AB*BD+%1M=3j131(+m),+89&'*>"H+ B + ->->>B*>"H+A >'*/8968O ¼Y w Y ¼Y Ä We NT ¬­6xºÇ§¯ ¬ xZÈ3 ¹Y« AT ®#É ° ¬ W¨Ê Y ¡ w Ä W j¬­pY § NT w ° ¬ W¨Ê Y ¢ w Ä WZY i8|8TN° ¬ Ë& Ãy/ ),o$6"3'*)~+m->/ 1(+,->+ABD-0/ B?'D+A),/m'?B E 0=3=3/8"( E8#B?/<-0'?=(G%'D1k=H+A92=(+89&#+6O Y ¡ WZY À ^M_*`KiATª¿­6x À f0g2^<iATk¯ ¿ x ¨° ¿ '*B ->J&'¨),/<:<J&B*/mEN+8B? O Ì Y ¡ Ì W Í Î6 x [8 nÏZ #|6{ i


!/21313/~->+ABD-0/ B*+8"3r'?B E8>"H13/8"( =(+89&78#92=3n+AB*B*+,->J&"3EN+6O Ð ¬ W Ì YY ¡¡ Ì W Y j|&À { i ^3_*` iAT ¿­ x j|&À { i f>g ^&i8T ¯ ¿ x j|& { i ° ¿ Ï Y |6{ À ^3_*` i8T ¿­ xo|&{ À f0g2^ iAT ¯ ¿ xo|&{½ ° ¿ Æ<»->+ABD-0/ B?/mBD+m:&>"('?EN+N=H+,:<>B¨E >"H1M/ "3r"3'D13$@>=M=3/~+8Bc=3>),$p/~/A=3=3>9678/6O t Ð T¬ W t Ð s ¿ Ñ t sT W¨Ê t Ð s¬ WeÒ Ó ¿ W t Ð ¿TÁÑ s P Ì Ì t )~+ Ô´Ô Õ W soP W Y ¡ t W #|&{ i t ¦<'*96:<t ' $@#" -0J&t ' O t Ð ¬T WZY\[<{ÖÇ!f0g2^2i8T ¿­ªY\[<{ÖÇ!^3_?`KiAT ¯ ¿ W¨Ê t Ð s¬ W t Ð T ¬ Ñ s P Ï Y |6{ [8a f0g2^2i8T ¿­ªY |&{½[AaX^M_*` i8T ¯ ¿ t t t '*B )m/<:<J6B?/ :<>B*B J&B?=3'*),/CE8>=M=(/8"( ¥d/8"(9&'*1(-0 $&"3/ $&"('?/~'*BSE >"H1M/ "3 Ó ¬ O Y~×>×>ØØ w(®(ÙÚ f>g ^&i8T ¿­cY ×#Ø ^3_?` i8Tª¯ ¿ ¶©ªB¨$6"3/<:</8=M=3/mE8>=M=(/8"('*+8B?r=3"H+ ' E8>"H13/8"(' Ð ¬ Ó ¬ "(>72+ABD+»'*9<¤69&n'*Bc=3#"3 #/ E ×#>"Ø w(®(HÙÚ 1M/ "3 Û ¿ Ü6 KÝ '?$&"(>9@:<'*+8),/ '¶"('D1MJ&B?=(+A=3' :<#B¶$&"(#-0j:<>92=(%j1M#"(->'? #'?/@ ©ªB E 0=M=(/8"(«ÔcÔ´ß ÕÞ WàÒ Ó ¿ j1k $6"3'*), B*+ "3#B*+8 >'*/89& -H &y+A96:<'D+A),/ + : J<=3'*B?'* > j+A"( $p>" "('D->+§EN+A"(!'?B E§+8B?/ "3 :&>B8"H+A7 78'*/ :&'c->J&"(E§+A=3J&"H+»"j !©ª9<¥U+N=3=3' BD+ ->/ 1M=(+A92=(\á6 % §âN"# !Æ >7 J&o-H 6\'*B "(+87878'*/»:<' -0J6"3EN+N=(J&"H+ EN+8B? Ä Ð ¿ ¼N¢ ã ã ä ² Wæåå t T Ñ s P åå W [<{ÖÇA[ åå t åå ç à +8B*->/8B*'*+8),/%'*),)mj:<'D+N=(+8),>92=3n'*B ENå+AB*/8"( :&>B*å B*+mE8#B?/<->'F=HG%E 0=3=3/8"('D+AB*r'D1k=H+A92=(+89&#+6O Y ¡ WeiN趿­§f0g2^ è T!YLiAèX¯ ¿ ^3_?` è T I2J&'*96:<' B +8-#-0>B*>"H+A #'?/ 9&oE§+8B? Y ¢ W Y iNè w ¿­8^M_*` è T Y«iNè w ¯ ¿ f>g ^ è T !#"¶E8#:&>"(K-H 6 '*B&E 0=M=(/8"(y$p/ 13'* >'*/89&KlK$@#"3$p>9@:<'*->/8BD+A"(¹+AB*B*+rE8#B?/<-0'?=(Go46+ 1k=H+r¥U+A"( '*B¨$&"(/<:</A=3=3/~1(->+ABD+A"(r=3"H+%'¨:&J&nE8>=M=3/ "3' O Y ¼ Ñ Y ¡ W iNè~f0g ^<è T ^3_*`Kè TSY«iNè~^M_*` è T<f0g ^<è T¶W | à +8B*->/8B*'*+8),/%'*9<¤69&n'*B¨$&"(/<:</A=3=3/,E8>=M=(/8"( ½Y ¼ é Y ¡ Wuêê iNè~^3¿­_?` è T iNè~f0¯ ¿g2^ è T °| ¿ êê W Y À ° ¿ è w êê iNè~f0g2^ è TëY iNèm^3_*`Kè Tì| êê ln#E '*:<#92=3 '?B¨¥U+N=M=(/ -H &nI2êê J&#1M=3/,EN+AB*/8"(r96/895:<'*$@#96:<»:&+8êê Bc=3>),$p/6


í6 K \96-H &;I2J&j1k=(/î#13>"H-0'* >'*/L13' "('*13/8B*E8}'*9º)~+89&'?#"(+«+896+AB*/872+& ïÅ J&9&'D->+î->/ 1(+.-H & -#+A)%4&'*+mBD+%¥d/8"(),+,:<#B?BD+%=3"H+A'*0=3=3/8"('D+& !Å +mE8#B?/<-0'?=(G6O Y ¡ W ¢ è ¿­Nf0g2^ è T Y«ð(è ¯ ¿ ^M_*`Kè T I2J&'*96:<' B +8-#-0>B*>"H+A #'?/ 9&oE§+8B? Y ¢ W Y ¢ è w ¿­A^3_*`Kè TSYîð(è w ¯ ¿ f0g2^ è T '*B ->J&'¨),/<:<J&B*/mEN+8B? Ì Ì Y ¢ Wïè w8ñ ¢ w ^M_*` w è T¨xÁð w f0g ^ w è T ò6 ¹Æ<'&=3"H+N=3=(+ :<'p-0/89@1M'D:<>"H+A"( '?B@)m/8=3/n:<#B?BD+ 46+A"H->+ ->/8),K¥d"3J&=M=3/»:&>B*B*+n->/8),$@/21M'* >'*/896 :&'X:<J& E >B*/<-0'?=(G& Æ -H 6'*+8),+8),/ ó}B +89&78/ B?/}-0/ ),$&"3j1M/ =("(+ BD+ :&'?"(> #'?/ 9&~:<>B*B*+ 4@+A"H->+} BD+5"(0=M=H+;-0/ 9&78'*J&9&7 >92=3~'*B $&J&92=3/ô:&'X$6+8"M=(>9& j+5CI2J&>B*B*/ô:<'X$@+A"3=3>96 #+&¦ +8B?B*/8"H+%/A=M=(>9&'*>),/~-H & Y ¡ W ¿­<R ¡8õªöM÷(÷(økù ø Y ¡8ú¸û´÷Hõªû ^3_*` ó V!Y ¯ ¿ ¡8ú¸û´÷Hõªû f0g2^ ó I2J&'*96:<'p4&'D1M/ 7896+»'?),$p/8"("3 -H &rB*+»E8>B*/<-0'?=(GnE 0=3=3/8"('D+AB* 1M/ )m)~+»13'D+»-0/ B?B*'?96#+A"( +AB*BD+ "(0=3=(+~->/89&7 '?J&9678>92=(n'S:<J&n$6J&92=3'S:&'S+N=3=3"H+8-#-0/6 KÆ nJ613'*+8),/~'?B 1M'D1k=(>)~+~:<'S"3'?¥d>"('F ),#9 =(/~'?),$&B*'D-0'?=3/ -H &»+ 1313/<-0'D+%+8B?BD¯ +,:<'?"(> #'?/ 9&n:<>B*BD+~-0/8"("(>92=3o'?B E8>"H13/8"( ¿­ »+AB*BD+ :&'?"(> #'?/ 9&n:<>B*B*+m"(0=3=(+m'?B E8>"H13/8"( ¿ ¦&+AB*B*/8"H+%13'?7 9&'?¤@->+,-H & O ¡êê R 8õªö3÷3÷Høªù ø Y ¿­ ¡8ú¸û´÷(õªû ^3_?` ó VüY ¡8ú ¯ ¿ û0÷(õªû °| ¿ êê We|»Ê êê | êêê ê¡8õªê öM÷(÷Høªù ø ¡8ú¸û´÷H| õªû Y ^M_*` ó W |»Êý^3_*` ó W ¡ õª¡ öMú¸÷(û´÷H÷Hê øªõªù û ø W i Å / 13$p/ 1M=(+A),#9 =(/ :<#B?BD+ 46+A"H->+ +§E2E '*>9& '?9«:<'*"3# >'*/89&%$@#"3$p>96:&'*->/8BD+A"(%+AB*BD+C-0/ "M "(>92=( :<>B8¤6J&),8¦j$@#"M=H+A92=3/¹$p>"S:<0=(>"()m'*96+8"3!'*BA=3#),$@/ '*),$&'*>7 +A=3/K$p>" B +N=M=("(+§E >"H13+8),>92=3/ lrÿ 9&#->#1(13+8"3'*/n-0/ 9&/ 1(-0#"3¹'*B6),/<:<J&B*/ :<#B?BD+»E >B*/ ->'F=HGn:<>Bc13'*1M=3#),+»46+A"H->+ þo-0/8"("(>92=3 9&/89}lnB J69&'*->/,)m/<:< / ´O Ì Y ¡ Ì ¡ õªöM÷(÷Høªù ø ¡ ú¸û´÷Hõªû ^M_*` ó V3wXx ¡ ú¸w û´÷Hõªû f0g ^ w ó W W v R Y W v ¡ õªw öM÷(÷(økù ø Yî[ ¡8õªö3÷(÷(øªù ø Ñ ¡8ú û0÷(õªû ^3_?` ó x ¡ ú w û0÷(õªû We[ Í [ 13>7 J&n-H & '?B¨=3>),$p/,=3/8=(+AB* l8O T¶W Ì Y ¡ Ì Ï §Ç<{ a Î s # 6 ÅS+r:&0¤69&'* >'*/896y:<' E8#B?/<->'F=HG ),#:<'D+o-0/8'*9 E8/ B?7 ¶'?B2=3#),$@/r=3/8=(+AB* XB*/o13$6+A #'?/ =3/A=H+AB*8¦ ->'?/ l O Ì Y ¡ ø û Ì s ö û *ø s Ä xÁs Ô W T ö û *ø W T Ä xîT w w Â


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