Mechanics
Projectile motion
I dimensional motion
Same as core physics up +
(2 =
x + 2as 20m S" . =
1SF
(2073 817/ 11)
=
v + 21 9 -
,
-
~
V =
24 8 m
.
Soon
,
& 25 m 5 . dom
= 20m S .
SF
V = Gt st
(20) ( 9 81)7
( 25)
= + -
-
.
t =
4 , 595/
= 55 SE
Rocket Boll
=
: :
vi = 23 + 2a)
S
=
Gl + 2ct2 =) Va =
Up
= (16 ,
0 02 =
(25572 + 2) -
3 17s
59(4)2 ()(4)
.
=
0(4) + =
127 0x104m
=
, 516 01
,
S =
1 ,
= S =
8a S =
24 S = xt + zat)
70'm
S =
Up (6)
+ 1 9
-
. 817/s)"
84 24
=
Total 11x103m Sp =
>B S =
Gha-176 50
-
Ax : R ,
2( =( Up
-
176 ,
58
VR
"
=
22 , 0725 m .
S
V = G + Gl
44 , /45 = 0 + G(4)
-
C
=
5 ,
518m . 5 = 6m . s
2 Dimension
Intial velocity has vertical horizontal components
Vo = Kost ,
Vy
= Using
No wind or air resistance
No horizontal acceleration
= 0 ..
a
U, be
Gravitational
-
Z
acceleration is 9 81m
.
.
s
Time for horizontal motion time for vertical motion
+x
ty
=
Often Vital link in
questions
Mange is horizontal distance
"vere =
4 SinD v2 = 2 + 2as
Opposite to math =
/21 8) Sin (32
,
9) ,
02 =
111 , 1281" + 2/ 9 81)s
State reference points
-
.
= 11 ,
128m . S
S = 6 3115m
E
,
the
right ~
.
g
.
up and to is
positive :
Staal =
18 , 5 M above grown
Swee :) 4
nor
= U cost 46
,
38
10 , 5 = =
(21 8) c0337 80
, ,
I
= 1, 809m .
S
t =
1 , 887s
no till
Snor() +
end Of =
/1802)(1 00 ,
Motion
=
33 ,
6056m
= 33 6
,
m
, A
X
Knur 3
D 128
=
2 I
+ 2 as of D
W Le
4x
Yvers
- Fin
(11 1287
=
vvorl =
,
+ 2( -
9 . 81)( -
4 , 20)
U14 , 36m . S" Or Vert = -4 , 36 m .
>
Ux = Ecos280 -15
=
N/A
Ver = 14 , 36 m . 3" down
Ta
14, 36
16 = 620289 =
8 .
5 m . S
"up
= F
Froo" Vot +
TcQ =
17 , 809 2 = 18 , 12
-
:
This
11 (1 8091 + ,
Q =
38 98 below
,
positive e-axis
=
~
22 8772m
1
at
-
,
·
S V= 4 +
: 22 9 m . S
,
0 =
8 .
5 + 1 -
9 81)7
.
7 : 0
.
875m
s =
(E) +
-288 =
(e)(0 .
=
3 7m ,
:
height- Imm ,
less then
SucMorun) 1s
26 =
)((1 5) .
Whor =16m S" .
right V
hor
=
UcosO Ver "
Using
=
=
1520360" 15 s in 30
T 5m 3 = 12 , 94m S
-
= . .
.
-
= Om 3 = 10 S
right
m
.
p
.
~
v2 = u + 2a)
0 =
18 +
2 -
9 81)3
.
S =
0 .
6m
-
~
P : Height
-
=
Use
* exact 11 to Q2
values from .
Only round for answers
M
>
. I
9
We h + zas
9
.2 .
93
L
9 4 .
"
02 Urer" 2(-9 81(4 U 0
U 9 8m
V 4
= + 001 =
at
. ,
.
.
dan = +
j
-8 , 85m . z
8 85 m 3" 5 ~ 8 (8 85) 1
=
Were 0m
=
Wer or
9 81)
=
Va cost 9
= +
.
-
,
:
N/ .
. .
= 8 85R S" up
19
.
, 9025
,
=
10 10362 t =
0
,
=
~ Using 4 , 6 ms"
right
=
ver
, 55
8 =
18 Sind
Speed =
4 6
,
m .
s
So
=
(e)
0 = 62 , 4
J - Li3) 10 9022
=
:
,
8 30 m
=
,
, > T
W
↑
t
1 1
.
.
1 2.
.
1 3
..
4 = 4 cos & Us : 4 Sind v
=
=
2
+ 2 as
Va
x S
of
=
(64) cos yo =
64Sin3 22 =
(7, 75)
2
+ 219 81/2. . 89 ye
=
63 52m S
,
.
=
7 79m
,
S
.
=
117 68 m s
,
.
E D
↳
s =
14 + 5
. =
Gl
+
a ha =
Wa
(33 52 52)7
+ 63 , 13
2(9
.
11 , 9 =
Sy
=
(7 79) 81)10 19) 2
=
+
. , ,
t = 0
,
195
~ =
1. 7 m 1 ,
63 = Fa 1, +
Tao o
=
0 187s : above net =
H 6812 17 7332 ,
+
,
0 :
8 85°
, belon #e-axis
,
=
117 , 95
~ 118 m S .
x
64 ,
4m .
5
&
Mar
3 .
1 . 1 . .I
3 .
2. .
3 1 3
.
..
U = =
8 , 20 m s . v =
13 + 2as
()
S 3
S
L "
114, 2) 02
- 2(9
81) by
= =
Y
+
.
ta 600 = ja 5
=
10 , 2x 10
, 3 =
)
-
~ = 10 t 1 , 455
~
↳= 3m
=
14 , 2 m .
S A , dow B C
S = (1)
/20(/1
+o .
=
,
43
=
11 867m
,
11 , 9 m
=
right
~
