-
g
O y y+ t 0= O t v y
v gt= y gt 2 1 2= …………………………………………………………
y y+ t 0= O t v y
v gt= - y gt 2 1 2= - ……………………………………………………l
y y+ v0 t v y
v v gt0= - y v t gt 2 1
0
2= - ………………………………………………
y y+ v0 t v y
v v gt0= + y v t gt 2 1
0
a a Wm =
a gm m= ` a g=
g g g g g

O x y xy t 0= O x+ v0
x v0 t vx x xvxx v vx 0= x v t0= …………………………………………………………… y g t vyyyvyy v→ vy
v gty= y gt 2 1 2= …………………………………………………………
xyt x /t x v0= y
y g v x
XQV51A-Z1Z1-02
6

O x y xy t 0= O x+ i v0
x cosv0 i
tvxx xvx x v0 → cosv0 i
cosv vx 0= i cosx v t0= i^ h ………………………………………………… y sinv0 i g- t vyy y vyy v→ vyv0 → sinv0 i
sinv v gty 0= -i siny v t gt 2 1
0
2= -i^ h …………………………………
xy t x / cost x v0= i^ h y
sin cos cos
/sin cosv g0
t t0=
v 0y= vy
sinv gt0 0 0= -i ` sin t
g
cos sin sin cos
sin sin sin sinv

v0m/s irad /0 21 1i r O x y x+ y+ gm/s2 ts vym/s ym vy= y= vxm/s xm vx= x= s lml= irad =i m x+
rad

v x0 v y0 cosvv x0 0= i sinvv y0 0= i …………………… cosv vx0 0= i^ h sinv vy0 0= i^ h g-
t vx vy
cosvv vx x0 0= = i …………………………………… sinv gtv v gty y0 0= - = -i ………………………… x y
XQV51A-Z1Z1-0
sinv t gty v t gt 2 1
2 1
2= - = -i ………………
s st t2 = mmy 0 =
sinv t gt0 2 1
0 2 2
cos cos sin
v2 0 2 0
= = ii i
lsin2 1=i i
2 2
=i r `
4 = r
g
=
/4=i r s st t2 = vxm/s vym/s
cosv v v 4 2
1 x 0 0= =
g
v
0 #= - = -
4 r
←t2 ← sin2i
sin cos2= i i


v m F tD v v+D tD F a
a t
F= D
D ………………………………………………
[]#[] m[]#[]
t mv
F= D
D ^ h ……………………………………………………………………
[]#[] []=[] …………………………l m l l

v+ =
- D
D^ h ∴ m v v mv F t+ - =D D^ h …………………
[]#[] []#[] tD
30
XQV51A-Z1Z1-06
10
m mdv Fdt=
t t1= t t2= v v1 v2
mdv Fdt v
t t1= t t2= F F FF F t t2 1-^ h
XQV51A-Z1Z1-0
11
v0m/s mkg sst 0 = sst t0 = / sst t3 20 = N s$ = + v0 mFt0 v0= N s$ vm/s = + vmFt0 v= e=[]/[] e= e

XQV51A-Z1Z1-0
12
FtI t F 2 1
2 1
m m v I Ft 2 1
0 1 00$ = =- - ^^ hh
N sI2 $
2 3
4 1

mv m I Ft 4 1
0 2 0$ = =- ^ h
/
← [] []

m1 m2 F F- tD v1 V1 v2 V2 m V m v F t1 1 1 1- = D m V m v F t2 2 2 2- = - D
m V m v m V m v F t F t 02 2 2 21 1 1 1- - = + -+ =D D^ ^ ^^h h h h ` m V m V m v m v1 1 2 2 1 1 2 2+ = +
tD []


30
XQV51A-Z1Z1-10
1
[]/[] v1 v2 V1 V2 v v2 1- V V2 1- v v2 1- V V2 1- ee
e v v
e v v
e v v
XQV51A-Z1Z1-11
15
x mAkg A mBkg B vAm/svBm/s vv BA2 A B x- x+ A B AB vAlm/svBl m/sAB A B ee= AB vAlm/s vBlm/svA =l vB =l v 0A 1l e2 A x- vBl1=20 B x+ x-

m v m v m v m vA A B B A A B B+ = +l l ………………………
v v
A B= - - -l l
` v v e v vA B A B- = - -l l ^ h ………………………… + mB# vAl m m v m v m v em v vA B A A A B B B A B+ = + - -l^ ^h h
` m m
A B
+ - - l
^ h
mA# vBl m m v m v m v em v vB A B A A B B A A B+ = + + -l^ ^h h
m m
A B
+ + - l
^ h
v m m
A B
+ - - 1l
^ h
` m v m v em v v 0A A B B B A B+ - - 1^ h
` m v v
B A B
v vA B2 vBl v 0B 2l
e B x+
← e
XQV51A-Z1Z1-12
16
irad v0m/s lm hm A gm/s2
h1m AA
A

17
x y
.11 51 °]i F F-t t F50N
.cos 0 981]i sin 1i
.0 20] .7 2 65] x x+ y y+
kg ·m/s x y x y


x A BW x+ A B MA MB x
A B U AVA A B VB
AVAMAMBVBW
M M3B A= V W2A= UMAW
x- VC MCC A C e
ACVA lVC
lMAVA MCVCe
e 1= VA lVC
l
gm/s2
ts s0= ts vym/s ymvyy
sinv v gty 0= -i …………………………………………………………………
sin t gty v 2 1 2
0 $ -= i ……………………………………………………………
v 0y= t t0=
sinv gt0 0 0= -i ` sin t
g
v 0
0= i
y h1= /sint t v g0 0= = i^ h
m msin sin sin sin
g
d n
ts vxm/s xmvxx cosv vx 0= i
cosx v t v tx 0 $= = i …………………………………………………………… A lm t1s
cos tl v 10 $= i ` s cos
s v l
= i
t t1= hm y1m
sin t gty v 2 1
1 1
tan cos
l h g
-i i^ h
y 0= t t2=
sin t gtv 2 1
0 2 2
s g

sin sin sin
v v
0
m/s m/scos sin vv v v v vx y
2 2
km m1 103= h s1 602=
/ m/skm h s m
#
# = =
P m/skg$ kg m/s . 3.0 N. kg m/s sP 0 15 20 3 0 $ # $$= = =^ h
IN s$ N s . . . N sI F 0 10 50 0 10 5 0 $ # # $= = =
xy
x . . .sin N sI 5 0 0 20 1 01# # $=]i
y . . .cos N sI 5 0 0 98 4 91# # $=]i
x pxkg m/s$ y pykg m/s$ x
sinI p Px1= - -i ^ h
` kg m/s . .sinP Ip 3 0 1 0x 1 $ = - + = - +i
. kg m/s2 0 $= -
` kg m/s . kg m/scosp I 4 9y 1 $ $= =i
pkg m/s$ kg m/s . . . . kg m/sp p p 2 0 4 9 2 7 2 2 65 5 3x y
2 2 2 2 $ # $= + = + =] ]
vm/s . .p v5 3 0 15#=]^ h ` m/s . m/sv 35 3 35 = g]
XQV51A-Z1Z2-05
21
VB l A B x+
V VB A1l A B VB V VV V V A BB B A = -= - ll
` V V VB A B= -l
VA M M W M V M V M V M V VA B A A B B A A B A B+ = + = + -l^ ^h h
` W M M
U M V M V M M W 2 1
2 1
2 1
2 2 2= + - +lc ^m h' 1
M M WM V M V V 2 1
2 1
2 1
2 22 - += + -^ ^h h' '1 1 ………………
M M3B A= V W2A=
V W M M
M M3B A= V W2A=
M WU M W M W W M M W 2 1
2 2 1
2
2
2 2 $ $= + - - + =^ c ^h m h( '2 1
A x+ C x- A C A x- C
x+ x+
M V M V M V M VA A C C A A C C- = - +l l …………
e V V
l
1 A
A C
+ - - l
1 C
A C
+ + - l
l
2 A
A C
- - l
^ h
2 C
A C
+ - l
^ h
XQV51A-Z1Z2-06