= Oplossingen vbtl 5 analyse 1, leerweg 4

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1 OPLOSSINGEN = Olossingn vtl nlys lrwg. D uliish ling (lz. ) _ + i + _ i + _ + i _ + i + _ i + _ + i + _ 8i _ + i + _ + i g ( _ + i + _ i + _ + i ) h i j Gr: gn D() = + k = k = g h i j 7 A() = + A() = g h 9 = ; = 0; = ; = = ; = ; = ; = ; = = ; = = ; = 0; = = ; = ; = 0 Q() = + R() = 0 Q() = + R() = 0 Q() = + R() = 0 Q() = R() = 0 Q() = R() = 9 Q() = + R() = 7 Q() = + R() = 8 Q() = R() = 0 Q() = 7 + R() = 0 Q() = + R() = + 9 g Q() = + + R() = + h Q() = R() = 0

2 i Q() = R() = j Q() = R() = 0 k Q() = + R() = l Q() = R() = m Q() = 0 R()= + n Q() = 0 R() = 0 A() = 8 + D() = + = 9 = = n = 7 = n = 8 = n = 9 = 0 n = 7; Q() = ; R() = 0 = n = ; Q() = + ; R() = + D A E A k = 9 k = 0 k = k = k = 0 k = o k = m = k = 7 k = 0 Q() = R() = 0 Q() = + R() = 7 Q() = R() = 0 Q() = R() = Q() = 9 + R() = 0 Q() = + + R() = 0 g Q() = + R() = 7 = n = = n = = n = = 8 n = 8 = n = 9 9 R() = + 0 R() = + R() = + + = = = = =. Dlrhi in R [] (lz. 8) Q() = + R() = 7 Q() = R() = 8 Q() = R() = Q() = + R() = Q() = R() = 0 Q() = + R() = g Q() = + + R() = 0 h Q() = R() = 9 i Q() = + R() = 0 Q() = Q() = + + ( + )( )( + ) ( + 7)( + )( ) ( )( ) ( + + ) ( + )( )( + )( + ) ( + )( )( ) ( )( 7)( + )( + ) g ( )( + )( ) h ( )( )( + ) i ( + )( )( ) j ( )( + )( + ) k ( ) ( + )( )

3 OPLOSSINGEN l ( + )( + )( ) m ( + )( )( ) n ( )( )( + ) 7 ( )( )( + ) (7 9)(7 + 9) ( )( + ) ( )( )( ) ( + ) ( ) _ + i_ i_ + i g ( + )( )( ) h _ + i_ i_ + i i ( + )( )( + ) j ( + )( )( + ) k ( + )( + + )( + ) l ( + )( + )( ) m ( )( + )( + )( + ) n ( )( ) o ( )( ) ( )( + )( )( + ) q ( )( ) r ( )( + ) s ( ) ( )( + + ) t ( )( + ) u _ + i_ i v ( )( + + )( ) w ( + )( ) ( )( )( + ) 8 ( )( + + ) ( + y)( y + 9 ) ( y)( + y)( + y + y )( y + y ) ( + )( + + 8) ( )( + + ) ( y)( + y + y + y + y + y + y ) g ( )( + )( + )( + ) h ( + )( ) 9 Q() = ; R() = Q() = ; R() = 9 Q() = ; R() = Q() = + + 8; R() = 0 Q() = ( ); R() = 0 B() = + 9 C() = D() = + + B D B C 7 A E() = + + F() = + G() = 7 + H() = 7 +. Vltrmuntis (lz. ) (); (); (0); g() gn 0 g h 0 + i gn j ; 0; V = C V = F < A 7 V = A A V = A 7 A + 7 V = 0 F < C 9 V = 7 A g V = F < F + < h V = A 7

4 i V = 7 A < F j V = A A k V = A A l V = A 7 ovn: A 7 A + 7 onr: A 7 A 7 ( ) Ç uur; 8 m uur n uur; m uur 7 ton: ( ); ( ) l: (0 ) 8 n u 0' " 0u; 0 m onr wtr u ' " 9 8 m En ilnj in ht min vn rivir 7 m 0 7u ' " u; 9 u; u; 7 vn u ' 8" tot u 8' " 8 m m 0 m m 87 m 9.00 u ; u ' " () = 8 + () = + + () = + 8 V() = + A m ls = 8 m; = m n h = 7 m 0 A I B III C II D IV A: noh vn noh onvn B: vn C: vn D: onvn () = + () = () = Jolin: 0 km/h; 7 km/h; km/h; 0 km/h Grt: 0 km/h; 8 km/h; 8 km/h; km/h Jolin: km/h; Grt: 8 km/h v(t) = (0 t) t! 70 0A mm /min V = litr A 0; 0 7 = 0 m; l = 08 m; h = 0 m litr miml orvlkt = 0 m ls = m 7 B 8 A 9 A 0 B A B 7 () = + 9

5 OPLOSSINGEN. Rtionl untis (lz. 8) om = R 0 ; nulw: + om = R \ # -; nulw: om = R \ # 0 -; nulw: # -; nulw 0 om = R \ om = R \ % /; nulw: 0 om = R \ # -; nulw: grik ; grik ; grik ; grik 000 uro uro 000 m jk() = C triultuur strt uit u min 0 s; vn u 7 min s tot u min s vn uur C in 0: 000 vossn in rio 0 tot vossn r kwrtl 7 8 minutn nn t + P Cl(t) 0 8 minutn 8 rst g ron 0u 9 min; tmrtuur: 7 C vn ngn g (t = 8) 0 () = + () = () = + () = h() = m hoog; 8 m lng m hoog; 7 m lng m hoog; m lng 0 m + l() = = 0; = ; y = y = = 0; = ; y = 0 = 0; y = = 0; = ; y = = ; = g = ; y = h = 0; y = = 0 = lr: lr: + 7 () = + ; nulw: () = _ i _ + i_ i 9 P() = 80 + n gn nulwrn 89 m; 78 m 0 () = _ + i 0 + n 0 m; uro () I; () II; () III; 8 () IV; () V; () VI; 7 () VII; () VIII () = + () = () = () = +

6 . Bwrkingn mt untis (lz. 99) g + + h i + 8 j g () = n + h () = i () = + + j nit omkrr 0 7 symmtrish t.o.v. rst isstri 8 nn k l = C R 0 D E C A () = nit omkrr nit omkrr () = + () = nit omkrr Mhtn (lz. ) 0 00 g h i 8 j y 0 0 n

7 OPLOSSINGEN g h 7 i j k + l 7 00 g 7 h 9 i j k l g h i j 79 vissoortn 80 m in ht klin gi tonm vn % = 8 0 _ s _ ii 7 = 0 uro 8 s = 9 t km 0 A.E. 9 m/s o 9 km/h 0 B A D A B E E 7 A 8 m. Eonntiël groi (lz. 9) gn; linir groi 9; 79; onntiël groi minutn st A: linir groi st B: onntiël groi mt groitor 0 N A = + 0 t; N B = 80 (0) t N A = ; N B = mr 0; in 0 Groirntg r mn voor ht vuln vn Thijs: % Groirntg r mn voor ht vuln vn Jonthn: 0 % Groirntg r jr % % 07 % % 0 % 00 % Groitor r jr Anm in rntn r jr % % 0 % % % 0 % Groitor r jr

8 jr jr N = 0 () t 87 miljon 7 tonm vn % r wk nm vn % r kwrtir groitor vn 077 r hluur 8 7 r uur 7 % N = 77 (7) t 80 triën % 8 miljon 0 009; n(t) = 000 (09) t 8 % % 79 uro 08 % D = (07) t mt t in gn (t = 0 o juli); 9 m m % 8 minutn 7 T(0) = 80 9 C 9 sonn HA: T(t) = 0 8 D uur (t Œ 8) 9 vrshuiving mt vtor () om = R; l = A + 7; is ln in R; HA: y =! 7 ; + 7 ()! A 8 7 () = () = k () = n () = + V = 7 % / V = ( V = % / V = # - V = ( V = % / g V = 8 ( h V = % / i V = # - V = # - V = # 0 - V = # - V = # - V = # 0- V = # - g V = # - h V = ( i V = # 0- j V = # 0 - k V = # - l V = # 0- m V = ( n V = # 0 - o V = # V = C 9 V = A A V = Ø V = A 7 V = A + 7 V = A 7 8

9 OPLOSSINGEN 8 V = # - V = % / V = A : jr gln jr gln; 900 vogls 800 vogls 9; ; 0 jr gln HA: n(t) = ; 00 vogls o lng uur. Logritmish untis (lz. ) stt nit 7 stt nit g 0 h 8 i 9 j k 0 l m n o = = = = = 8 = 0 g = h = = 9 = = = = 0 = log + log y log z ( log + log y log log z) log log y log z log + log y log z 0 7 log y log z y y log z 9 () = log( ) () = log( + ) () = () = 0 A R 0 A 07 A + 7 A 7 A 7 A + 7 A 7 R \ ( 0 g A + 7 h i A 7 A 7 j A om = A + 7; om g = A 7 A( 8; 7) n B(; 09)! A ; 8 A 7 ; 7 = = = = = = = = = = = 0 = 9

10 jr 98 jr 7 gn 8 N B = (0) t N V = 8 (0089) t N B = 9 miljon; N V = 07 miljon jr 9 % 0 vóór Christus 0 wkn mg R E = kilojoul C R = v = 87 km/h n = 00 V = # - V = # 8- V = ( + V = # - V = # 0- V = # - g V = # - h V = # - V = # 77- V = # 7- V = # - V = ( V = # 7 7- V = # - g V = # 0 999; - h V= ( 87 i V = # - V = # V = # - V = # V = # 980- V = # 8- V = # g V = # h V = # 9- i V = A ; V = A A V = A 7 A + 7 V = A 7 A + 7 V = A V = F 9 < V = < < 8 n = 0 (9) t gn 9 t = 8 N * = 99 (0) t N = t + 99 _ 0 i 0 N = 000 t + _ 0 i 7 mnn N(t) = 0 t + _ 0 7i 87 vrs 0 jr N(t) = 0 t + _ 0 0i 8 m E 9 wkn 7 gn 8 0

11 OPLOSSINGEN g 8 h i 8 j k 8 0 l 0. D lgmn sinusunti (lz. 97) g h i r r 8 r r r r 7 r r r g 70 h 80 i r 0807 r 00 r 99 r 98 r r g 8898 r h 08 r i 008 r g 0 h 0 i 7 " r r; ' " 7 rio = 8 8 A(; 087 ) B k C _ 0i D n E n F( ; 0 ) 0 rio = ; mlitu = i() grik () grik h() grik g() grik rio = rio = rio = rio = mlitu: rio: svrshil: vnwihtslijn: y = 78 sonn 0 mtr 7 son mi; 98 C 0 C 0 C gn 08 gn ' 0" ' 0" 8 ' 7" 8 ' 0" ; ; 0; y = ; ; 0; y = ; ; ; y = 0 0; ; ; y =

12 0 8; ; y = 0 ; ; ; y = 8 8 () = sin < + nf + ; ; () = sin ; ; () = sin ( ); ; 0 () = sin + () = sin 9 k C () = sin () () = sin 9 k + 8 C 8 mtr u min 09 s; u min 7 s vn 9u tot u min 8 s; nn 7 = ; = 0; = 0; = uitvrn: u 7 min s; trugkrn: u min s 8 D. Som n vrshilormuls (lz. 09) sin os tn ot sin os 8 tn os tn 0 sin sin sin 0 sin 0 sin ( + + g) = sin os os g + os sin os g + os os sin g sin sin sin g os ( ) = 8 8 sin ( + ) = 77 8 tn ( ) = 8 os ( + ) = sin ( ) = tn ( + ) = A. Vrulings n hlvringsormuls (lz. ) sin = ; os = 7 ; tn = 7 sin = ; os = ; tn = sin = 0 + ; os = ; tn = sin = sin os 8sin os os = 8os + 8os tn = tn tn tn + tn 7 sin = = 088 os = + = tn = = 0 sin = + = 0998 os = = tn = = sin = os = tn =

13 OPLOSSINGEN 8 () = sin kc () = sin < + nf+ 8 () = sin 9 A 0 D C. Formuls vn Simson (lz. 8) sin os os 7 sin os os os sin sin sin sin os g sin sin h sin sin os sin os os sin sin sin os tn os os ot tn os os os D os 8 + os sin( ) + sin( + ) sin( + ) + sin( ). Goniomtrish vrglijkingn (lz. 7) V =! ( + mt k! Z V = % + mt k! Z/ V = # ; mt k! Z- V = % + mt k! Z/ V =! 8 ( + 8 mt k! Z V = # 7 + ; 97 + k mt k! Z- g V = # 0' + 0 ; mt k! Z- h V = # + 80 mt k! Z- i V = #! + 80 ; ; mt k! Z- j V = % + mt k! Z/ V = ; ( + + mt k! Z 9 V = ; % + + mt k! Z/ V = mt k! Z \ % + / ( V = % + ; + mt k! Z/ V =! ; ( + ; mt k! Z V = % mt k! Z/ g V = % + _ mt k Z + i! / h V = ; ( + ; + mt k! Z i V = #! mt k! Z- j V =! % + mt k! Z/ k V = ;! ( + + ; + mt k! Z/ l V = # mt k! Z- m V = # mt k! Z- n V = ( + + mt k! Z 0 V = ; ; ( mt k! Z V =! ;! % + + mt k! Z/ V =! ;! ( + + mt k! Z 0 0 V =! % + ; _ k+ i mt k! Z/ V = % + mt k! Z/ V =! % + mt k! Z/ g V = # ; ; mt k! Z- h V = % mt k! Z/ i V = ( + mt k! Z j V = ( mt k! Z

14 k V = ; ( + + mt k! Z l V = # mt k! Z- A n n B n nulwrn vn : k mt k! Z t = 0; t = 08; t = ; t = 708 in 70 0A rst kr: vn u min s tot 0u 0 min s tw kr: vn u min s tot u min 8 s 7 n 8 s n n s 8 o ril n o juni 9 u min 8 s 79 m 0 70 konijnn; vossn vn stmr 00 tot 9 juni 0 vn 0/0/00 tot 0/0/00 n vn 0//0 tot 0/0/0 ysik: (t) = 0 sin t n motionl: (t) = 0 sin t n 8 intlltul: i (t) = 0 sin t n gn 7 gn ; 0; 99 novmr vn u ' 09" tot u 9' " vn u ' " tot u ' 8"

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