(1) The document analyzes linear motion, circular motion, and parabolic motion using vectors. It discusses position and displacement vectors and how to represent them. (2) It provides an example problem involving the displacement vector of a particle moving in one dimension. (3) The goal is for students to be able to analyze natural phenomena and patterns within the scope of classical mechanics.
Oelheld, Cutting Oil, Metal Cutting Oil Distributor-OmkarsupraDCPL
Oelheld Germany, are lead innovators in fluid technology with a vast application and product base in metal cutting oils, spindle coolants (anti corrosive & anti freezing oils) and dielectrics
Oelheld, Cutting Oil, Metal Cutting Oil Distributor-OmkarsupraDCPL
Oelheld Germany, are lead innovators in fluid technology with a vast application and product base in metal cutting oils, spindle coolants (anti corrosive & anti freezing oils) and dielectrics
Влияние оральных контрацептивов на кожу пациенток при комбинированном лечении...kpyu
Рассматривается влияние оральных контрацептивов на кожу. Приведены результаты клинического наблюдения за пациентами 18-25 лет, препараты Джес и Ярина для улучшения состояния кожи при себорее и акне I-II степени тяжести.
Влияние оральных контрацептивов на кожу пациенток при комбинированном лечении...kpyu
Рассматривается влияние оральных контрацептивов на кожу. Приведены результаты клинического наблюдения за пациентами 18-25 лет, препараты Джес и Ярина для улучшения состояния кожи при себорее и акне I-II степени тяжести.
Fleet management these days is next to impossible without connected vehicle solutions. Why? Well, fleet trackers and accompanying connected vehicle management solutions tend to offer quite a few hard-to-ignore benefits to fleet managers and businesses alike. Let’s check them out!
In this presentation, we have discussed a very important feature of BMW X5 cars… the Comfort Access. Things that can significantly limit its functionality. And things that you can try to restore the functionality of such a convenient feature of your vehicle.
What Does the PARKTRONIC Inoperative, See Owner's Manual Message Mean for You...Autohaus Service and Sales
Learn what "PARKTRONIC Inoperative, See Owner's Manual" means for your Mercedes-Benz. This message indicates a malfunction in the parking assistance system, potentially due to sensor issues or electrical faults. Prompt attention is crucial to ensure safety and functionality. Follow steps outlined for diagnosis and repair in the owner's manual.
Comprehensive program for Agricultural Finance, the Automotive Sector, and Empowerment . We will define the full scope and provide a detailed two-week plan for identifying strategic partners in each area within Limpopo, including target areas.:
1. Agricultural : Supporting Primary and Secondary Agriculture
• Scope: Provide support solutions to enhance agricultural productivity and sustainability.
• Target Areas: Polokwane, Tzaneen, Thohoyandou, Makhado, and Giyani.
2. Automotive Sector: Partnerships with Mechanics and Panel Beater Shops
• Scope: Develop collaborations with automotive service providers to improve service quality and business operations.
• Target Areas: Polokwane, Lephalale, Mokopane, Phalaborwa, and Bela-Bela.
3. Empowerment : Focusing on Women Empowerment
• Scope: Provide business support support and training to women-owned businesses, promoting economic inclusion.
• Target Areas: Polokwane, Thohoyandou, Musina, Burgersfort, and Louis Trichardt.
We will also prioritize Industrial Economic Zone areas and their priorities.
Sign up on https://profilesmes.online/welcome/
To be eligible:
1. You must have a registered business and operate in Limpopo
2. Generate revenue
3. Sectors : Agriculture ( primary and secondary) and Automative
Women and Youth are encouraged to apply even if you don't fall in those sectors.
"Trans Failsafe Prog" on your BMW X5 indicates potential transmission issues requiring immediate action. This safety feature activates in response to abnormalities like low fluid levels, leaks, faulty sensors, electrical or mechanical failures, and overheating.
What Exactly Is The Common Rail Direct Injection System & How Does It WorkMotor Cars International
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Ever been troubled by the blinking sign and didn’t know what to do?
Here’s a handy guide to dashboard symbols so that you’ll never be confused again!
Save them for later and save the trouble!
Things to remember while upgrading the brakes of your carjennifermiller8137
Upgrading the brakes of your car? Keep these things in mind before doing so. Additionally, start using an OBD 2 GPS tracker so that you never miss a vehicle maintenance appointment. On top of this, a car GPS tracker will also let you master good driving habits that will let you increase the operational life of your car’s brakes.
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𝘼𝙣𝙩𝙞𝙦𝙪𝙚 𝙋𝙡𝙖𝙨𝙩𝙞𝙘 𝙏𝙧𝙖𝙙𝙚𝙧𝙨 𝙞𝙨 𝙫𝙚𝙧𝙮 𝙛𝙖𝙢𝙤𝙪𝙨 𝙛𝙤𝙧 𝙢𝙖𝙣𝙪𝙛𝙖𝙘𝙩𝙪𝙧𝙞𝙣𝙜 𝙩𝙝𝙚𝙞𝙧 𝙥𝙧𝙤𝙙𝙪𝙘𝙩𝙨. 𝙒𝙚 𝙝𝙖𝙫𝙚 𝙖𝙡𝙡 𝙩𝙝𝙚 𝙥𝙡𝙖𝙨𝙩𝙞𝙘 𝙜𝙧𝙖𝙣𝙪𝙡𝙚𝙨 𝙪𝙨𝙚𝙙 𝙞𝙣 𝙖𝙪𝙩𝙤𝙢𝙤𝙩𝙞𝙫𝙚 𝙖𝙣𝙙 𝙖𝙪𝙩𝙤 𝙥𝙖𝙧𝙩𝙨 𝙖𝙣𝙙 𝙖𝙡𝙡 𝙩𝙝𝙚 𝙛𝙖𝙢𝙤𝙪𝙨 𝙘𝙤𝙢𝙥𝙖𝙣𝙞𝙚𝙨 𝙗𝙪𝙮 𝙩𝙝𝙚 𝙜𝙧𝙖𝙣𝙪𝙡𝙚𝙨 𝙛𝙧𝙤𝙢 𝙪𝙨.
Over the 10 years, we have gained a strong foothold in the market due to our range's high quality, competitive prices, and time-lined delivery schedules.
Symptoms like intermittent starting and key recognition errors signal potential problems with your Mercedes’ EIS. Use diagnostic steps like error code checks and spare key tests. Professional diagnosis and solutions like EIS replacement ensure safe driving. Consult a qualified technician for accurate diagnosis and repair.
Core technology of Hyundai Motor Group's EV platform 'E-GMP'Hyundai Motor Group
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Maximized driving performance and quick charging time through high-density battery pack and fast charging technology and applicable to various vehicle types!
Discover more about Hyundai Motor Group’s EV platform ‘E-GMP’!
Core technology of Hyundai Motor Group's EV platform 'E-GMP'
02 bab1
1. Bab
1
Meriam dengan peluru manusia ditembakkan dengan sudut kemiringan dan kecepatan
awal tertentu agar peluru jatuh tepat pada sasaran.
1
Analisis Gerak
A. Persamaan Gerak
Lurus
B. Gerak Parabola
C. Gerak Melingkar
Hasil yang harus Anda capai:
menganalisis gejala alam dan keteraturan dalam cakupan mekanika benda titik.
Setelah mempelajari bab ini, Anda harus mampu:
(7C@3:=3: @63 ?7;:3E 3EC3=D; ?7C;3? 67@93@ B7FCF ?3@FD;3
*33: D3EF =7A?BA= D;C=FD J3@9 E7C=7@3 67@93@
3EC3=D;
@J3 E3:F@
20. =?
x (km)
U
T
R
B
A
B
A
30°
Sekolah Tarigan
7
12
0
r2
r1
Dr
112,7°
–5
–5
3
8
y
x
Gambar 1.4
Ax dan Ay merupakan komponen-komponen
vektor A pada sumbu-x
dan sumbu-y.
Contoh 1.1
Contoh 1.2
Penulisan notasi vektor yang benar
adalah dengan tanda panah di atas atau
dengan huruf tebal.
P = P.
Dalam buku ini digunakan huruf tebal
sebagai penanda vektor.
x
y
Ay
A
Ax
0
22. 63@
P67@93@
63@
G7=EAC =757B3E3@ C3E3C3E3 633? 6F3 6;?7@D; 3633:
3 ' (
P
Gambar 1.5
Kecepatan rata-rata v di antara A
dan B searah dengan arah r .
0
r1
r2
y
x
A, t1
B, t2
(AD;D;E;E;=63B3E6;EF;D=3@D74393;47C;=FE
39. N
?D
?D
-7=EAC=757B3E3@4FCF@93633:
3 ' (
'
(?D
r'
r2
B', t2'
B, t2
r
Gambar 1.7
v
r''
r2''
B'', t2''
r2'
A, t1
v
Kecepatan sesaat suatu benda dapat
diperoleh dari garis singgung kurva
lintasan benda untuk satu dimensi.
v
Gambar 1.8
Grafik kecepatan sesaat pada bidang
xy atau bidang dua dimensi.
6 Mudah dan Aktif Belajar Fisika untuk Kelas XI
3
d
t dt
P
*753C3 ?3E7?3E;D D7DF3; 67@93@ E38D;C3@ 97A?7EC;D F@EF= EFCF@3@
EFCF@3@ B7CE3?3 63C; DF3EF 8F@9D; B363 DF3EF E;E;= 3633: 9C36;7@ 93C;D
D;@99F@9 =FCG3 6; E;E;= E7CD74FE 7@93@ 67?;=;3@ =757B3E3@ D7D33E
63C; DF3EF E;E;= ?3E7C; 63B3E 6;E7@EF=3@ D753C3 9C38;= 3B34;3 6;=7E3:F;
9C38;= B7CB;@63:3@ E;E;= ?3E7C; E7C:363B H3=EF
(7C:3E;=3@ +! / ,@EF= 9C38;= B7CB;@63:3@ E7C:363B H3=EF
633?97C3=D3EF6;?7@D;63B3E6;=7E3:F;47D3C=757B3E3@D7D33E47@63;=3
93C;D D;@99F@9 =FCG3 6; DF3EF E;E;= ?7?47@EF= DF6FE E7C:363B DF?4F-
47D3C =757B3E3@ D7D33E 47@63 E7CD74FE 63B3E 6;EF;D D74393; 47C;=FE
E3@
P
+! / ?7?B7C;:3E=3@ D74F3: E;E;= ?3E7C; B363 4;63@9
-7=EAC =757B3E3@ D7D33E@J3 3633: 3 ' ( D763@9=3@ 47D3C@J3
?7@36; =73F3@ D7D33E #73F3@ D7D33E 6;B7CA7: 67@93@ B7CD3?33@
P
63BF@ 3C3: =757B3E3@ D7D33E B363 4;63@9 67@93@ ?7;:3E =757B3E
3@B363DF?4F-3633:63@=757B3E3@B363DF?4F- 3633: D7:;@993
3=3@ 6;B7CA7:
E3@
P
36; =73F3@ B363 DF?4F- 63@ DF?4F- 3633:
5AD 63@ D;@
P
40. #7E7C3@93@
=73F3@ B363 DF?4F- ?D
=73F3@ B363 DF?4F- ?D
x
y
vy
vx
v sin
v cos
x
garis
singgung
t
y = x(t)
v sesaat
y
x
vy j
v = 20 m/s
vx i
37°
Gambar 1.6
Ketika B makin dekat dengan A atau
lim
t
0
, kecepatan sesaat v di A
menyinggung lintasan di A.
r1
y
0 x
Contoh 1.4
0
0
0
41. Analisis Gerak 7
3?43C6;D3?B;@93633:9C38;=B7CB;@63:3@
D74F3:D7B763J3@947C97C3=E7C:363BH3=EF
+7@EF=3@=757B3E3@D7B763B363D33E
3
43. D7=A@9C38;=97C3=PD7B76347C363B36393C;DFCFD
7D3C=757B3E3@D7B3@3@993C;DE7CD74FE3633:
E3@
?
D
?D
4 (363D33ED7=A@9C38;=97C3=PD7B76347C363B36393C;DFCFD
7D3C=757B3E3@@J33633:
E3@
D
D7B763E;63=47C97C3=
5 (363D33E
D7=A@D7B76347C363B36393C;DFCFD#757B3E3@D7B763
?7CFB3=3@=7?;C;@93@93C;DJ3;EF
E3@
?
D
P
?D
+3@63@793E;8?7@F@F==3@D7B76347C43;=3C3:
6 0
3
30
A
B C
D
6 8 10 14 15 t (s)
Contoh 1.6
*74F3:B3CE;=747C97C3=67@93@B7CD3?33@;@E3D3@/
44. P
?67@93@
633??7E7C63@633?D7=A@+7@EF=3@=757B3E3@B3CE;=7=7E;=3D7=A@
4 !
#757B3E3@6;B7CA7:63C;6;87C7@D;3B7CD3?33@BAD;D;7@93@?7?3DF==3@H3=EF
6;B7CA7:
c. Menghitung Posisi dari Kecepatan
+73: @63 =7E3:F; 43:H3 =757B3E3@ ?7CFB3=3@ EFCF@3@ B7CE3?3
63C; 8F@9D; BAD;D; J3;EF 3
/
' ( *753C3?3E7?3E;D BAD;D;
D74F3: B3CE;=7 63B3E 6;B7CA7: 63C; 8F@9D; =757B3E3@@J3 ?73F; BCAD7D
;@E79C3D;
7D3C =757B3E3@ 633? 3C3: DF?4F-
P
P
/
48. ''?D
Tantangan
untuk Anda
Pada saat balapan A1-GP, pembalap
Indonesia, Ananda Mikola memantau
kecepatannya melalui speedometer.
Menurut Anda, bagaimanakah cara
kerja speedometer? Gunakan bahasa
Anda sendiri untuk menerangkan cara
kerja speedometer.
0
60. Gambar 1.9
(a) Grafik fungsi kecepatan (v)
terhadap waktu (t).
(b) Grafik v–t untuk gerak benda
yang berbalik arah.
Contoh 1.7
P
t1
t2 t3
v
t
4
0
v (t)
t
2
1
v(t)dt
t1 t2
a (t)
3
0
61. –4 –3 –2 1 2 3 4 5
v
t
Contoh 1.8 v (m/s)
8
7
6
5
4
3
Analisis Gerak 9
#757B3E3@B3CE;=7J3@947C97C3=FCFD?7?7@F:;B7CD3?33@3
93. ?
Tugas Anda 1.2
Diskusikan dengan teman
sebangku Anda, apa perbedaan
antara jarak dan perpindahan?
Bagaimana Anda menerangkan
konsep jarak dan perpindahan ini
pada kasus mobil F1 yang sedang
balapan di sirkuit? Pada balapan
F1, garis start dan finish berada di
tempat yang sama, dan mobil
hanya bergerak mengelilingi
sirkuit.
4. Percepatan
*7E;3B 47@63 J3@9 ?7@63B3E 93J3
3=3@ ?7@933?; B7CF43:3@
=757B3E3@ D7:;@993 47@63 E7CD74FE ?7?;;=; B7C57B3E3@ *3?3 :3@J3
67@93@ =757B3E3@ B363 B7C57B3E3@ 6;=7@3 F93 ;DE;3: B7C57B3E3@ C3E3
C3E363@B7C57B3E3@D7D33E'7:=3C7@3=757B3E3@E7C?3DF=47D3C3@G7=EAC
?3=3B7C57B3E3@F93?7CFB3=3@47D3C3@G7=EACJ3@9@;3;@J3?7CFB3=3@
EFCF@3@ B7CE3?3 63C; =757B3E3@ ,@EF= 47@63 J3@9 47C97C3= G7CE;=3 =7
3E3D B7C57B3E3@ J3@9 6;?;;=; 3633: B7C57B3E3@ 9C3G;E3D; 63@ 47C@;3;
@793E;8 D763@9=3@ F@EF= 97C3= 3EF: B7C57B3E3@@J3 47C@;3; BAD;E;8
a. Percepatan Rata-Rata
(7C57B3E3@C3E3C3E3B36397C3=6F36;?7@D;?7?;;=;B7@97CE;3@D3?3
67@93@ B7C57B3E3@ C3E3C3E3 B363 97C3= D3EF 6;?7@D; J3;EF :3D; 439;
B7CF43:3@ =757B3E3@ E7C:363B ;@E7CG3 H3=EF
+! / ?7?B7C;:3E=3@ 9C38;= :F4F@93@ =757B3E3@ E7C:363B
H3=EF (363 D33E
47@63 47C363 6; E;E;= 67@93@ =757B3E3@ J3@9
6;?;;=;
(363 D33E 47@63 47C363 6; E;E;= 67@93@ =757B3E3@ J3@9
6;?;;=; (7C57B3E3@ C3E3C3E3 47@63 63C; D3?B3; 3633:
P
#7E7C3@93@
B7C57B3E3@ C3E3C3E3 ?D
B7CF43:3@ =757B3E3@ ?D
D73@9 H3=EF D
v2
v1 A
Gambar 1.10
Percepatan rata-rata.
B
t1
t2
t
v
a =
v
t
t (s)
–1
2
–1
0
–2
–3
–4
–5
–6
–7
–8
–9
–10
–11
–12
1
v = 3t2 – 6t – 9
94. -7=EAC B7C57B3E3@ D74F3: 47@63 J3@9 47C97C3= B363 4;63@9 J3;EF
B363DF?4F:AC;KA@E3DF?4F-63@DF?4FG7CE;=3DF?4F- @;3;@J3
3633:
0
lim
t t
v a
t2
v a
v1
10 Mudah dan Aktif Belajar Fisika untuk Kelas XI
a'a (
P
63BF@ 47D3C B7C57B3E3@ C3E3C3E3 ?7?7@F:; B7CD3?33@
2 2
ax ay
P
#7E7C3@93@
B7C57B3E3@ C3E3C3E3 ?D
a 47D3C B7C57B3E3@ B363 DF?4F- ?D
a 47D3C B7C57B3E3@ B363 DF?4F- ?D
b. Percepatan Sesaat
*7B7CE;B363=757B3E3@D7D33EB7C57B3E3@D7D33E97C3=D74F3:B3CE;
=7 ?7?4FEF:=3@ D73@9 H3=EF J3@9 D3@93E D;@9=3E J3;EF
?7@67=3E; @A 36; B7C57B3E3@ D7D33E ?7CFB3=3@ EFCF@3@ B7CE3?3 63C;
B7CD3?33@ =757B3E3@ F@EF= D73@9 H3=EF ?7@67=3E; @A
;?
;?
d3
3t
dt
P
(7C57B3E3@D7D33E?7CFB3=3@EFCF@3@=76F363C;8F@9D;BAD;D;=3C7@3
3
/
'7: =3C7@3 ;EF
3
/
P
+3:F=3: @63 53C3 ?7@F@F==3@ BCAD7D ;?;E 633? ?7@7@EF=3@
B7C57B3E3@D7D33E47C63D3C=3@9C38;=,@EF=?7@97E3:F;@J3B7C:3E;=3@
+! /
(363 +! / 63@ +! / ! G7=EAC 3
63@ 3
?7CFB3=3@ G7=EAC =757B3E3@ B363 D33E
63@ D763@9=3@ 3 ?7CFB3=3@
B7CF43:3@ =757B3E3@
6;4F3E E7E3B D763@9=3@ 6;4F3E ?7@67=3E;
D7:;@993 7C63D3C=3@678;@;D;
3
?7?;;=; 3C3: J3@9 D3?3
67@93@ 3'7:=3C7@3 ;EF ?7?;;=;3C3:J3@9 D3?367@93@3=7E;=3
?7@67=3E;@A(363 D33E 6;53B3; D7B7CE;6;EF@F==3@ +! /
63@3
6;EF@F==3@67@93@63@3D7:;@993 ?7@36; -7=EAC
B7C57B3E3@ D7D33E D73F ?7@36; D;D; 7@9=F@9 ;@E3D3@ E;E;= ?3E7C;
D763@9=3@ G7=EAC =757B3E3@ 3 E7E3B ?7@J;@99F@9 ;@E3D3@ 6;
;=3B3CE;=747C97C3=B3634;63@9 6;63B3E=A?BA@7@=A?BA@7@
B7C57B3E3@ 47C;=FE ;@;
3 ' ( d d
dt dt
' ( ' ( x y dv dv
dt dt
@63 E7@EF E73:?7@97E3:F; 43:H3 63@
7@93@ 67?;=;3@
63@
2 2
2 2
d x d y
dt dt
D7:;@993 ' (
P
Gambar 1.11
Percepataan sesaat a =
v
merupakan percepatan pada saat
t2 – t1 menuju nol atau t menuju
nol.
3
4
5
y
x
v2
v1
v1 t1
v2
t
v2
v1
t
y
x
a
t1
v2
t2
0
0
y
x
t
0
v
95. t
Analisis Gerak 11
*74F3:B3CE;=747C97C3=67@93@B7CD3?33@=73F3@
P67@93@
633??D63@633?D7=A@+7@EF=3@3:
3 47D3CB7C57B3E3@C3E3C3E397C3=B3CE;=7F@EF=DD3?B3;67@93@
D
4 47D3CB7C57B3E3@3H3B3CE;=763@
5 47D3CB7C57B3E3@B3CE;=7B363D33E
96. D7=A@
4 !
3 (7CD3?33@=757B3E3@3633:
P
,@EF=
D
P ?D
,@EF=
D
P
?D
a
?D
4 (7CD3?33@B7C57B3E3@6;B7CA7:63C;EFCF@3@B7CE3?3B7CD3?33@=757B3E3@J3;EF
d
dt
P P
7D3CB7C57B3E3@3H3B3CE;=7B363D33E 3633:
P PP?D
5 7D3CB7C57B3E3@B3CE;=7B363D33E
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Informasi
untuk Anda
Information for You
12 Mudah dan Aktif Belajar Fisika untuk Kelas XI
'
'
112. PP
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D7=A@3C3=E7C3F:63B3E
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Contoh 1.11
Pada 26 September 1993, seorang
mekanik mesin diesel bernama Dave
Munday yang untuk kedua kalinya
melakukan aksi jatuh bebas setinggi
48 m di air terjun Niagara yang
berada di wilayah Kanada. Pada
aksinya itu, ia menggunakan sebuah
bola baja yang diberi lubang udara
supaya ia bisa bernapas ketika berada
di dalamnya. Munday sangat
memperhatikan faktor keselamatan
pada aksinya itu karena sudah 4
orang yang tewas ketika melakukan
aksi serupa. Oleh karena itu, ia
memperhitungkan aspek fisika
(terutama gerak lurus) dan aspek
teknis dari bola baja yang
digunakannya.
On September 26th, 1993, Dave Munday
a diesel mechanic went over the
Canadian edge of Niagara Falls for
the second time. Freely falling 48 m to
the water (and rocks) below. On this
attempt, he rode in a steel ball with a
hole of air. Munday keep on surviving
this plunge that had killed four other
stuntman, had done considerable
research on the physics (motion along
a straight line) and engineering
aspects of the plunge.
Sumber: Fundamental of Physics, 2001
113. Analisis Gerak 13
5. Perpaduan Dua Vektor
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Tugas Anda 1.4
Buatlah kelompok diskusi kecil.
Apakah Anda dan teman-teman
dapat memprediksi gerak seperti
apa yang dihasilkan oleh
perpaduan dua buah gerak lurus
berubah beraturan? Setelah
selesai diskusi, kemukakan
pendapat kelompok Anda di
depan kelas.
Gambar 1.13
v adalah vektor resultan dari v1
(kecepatan aliran sungai) dan v2
(kecepatan perahu).
Contoh 1.12
*74F3:B7C3:F:7@63=?7@J747C3@9;DF@93;67@93@=757B3E3@
119. ?
Kata Kunci
• arah vektor
• besar vektor
• jarak
• kecepatan
• kelajuan
• percepatan
• perpindahan
• posisi
• vektor satuan
v
v2 (kecepatan perahu)
v1 (aliran sungai)
vp
vs
v
s
120. Tes Kompetensi Subbab A
$/( ) ,* # * +!2)2* 1' ,
bola (A) bola (B)
Sumber: Physics for Scientist
Engineers, 2000
14 Mudah dan Aktif Belajar Fisika untuk Kelas XI
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Tokoh
Galileo Galilei
(1564–1642)
Galileo Galilei lahir di kota Pisa, Italia,
pada 15 Februari 1564. Ia belajar
kedokteran di Universitas Pisa. Oleh
karena ia lebih tertarik dengan ilmu
alam, ia tidak melanjutkan belajar
kedokterannya, tetapi belajar
matematika. Ia meninggalkan Pisa
untuk belajar di Universitas Padua. Ia
adalah pendukung teori Heliosentris
yang menyatakan bahwa Matahari
adalah pusat tata surya. Penemuan
Galileo yang terkenal adalah
teleskop dan menemukan
pegunungan di Bulan serta satelit di
Yupiter. Oleh karena hobinya
mengamati benda-benda langit
termasuk Matahari, ia menderita
kebutaan pada usia 74 tahun. Ia
meninggal dunia 4 tahun kemudian
pada usia 78 tahun.
y
v0 sin
O(0,0)
v0
vy
vx
v0 cos
vy = 0
ay = –g
vy
vx
v
v
vy
x
vx
149. N 3=3@ ?7@9:3D;=3@ 3C3= E7C3F: J3@9 D3?3 (363 93?43C
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N
Gambar 1.16
Grafik lintasan sebuah benda
dengan sudut elevasi berbeda dan
kecepatan awal yang sama.
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y jarak vertikal (m)
x jangkauan
(meter)
75°
60°
45°
15°
Contoh 1.14
Tantangan
untuk Anda
Apakah tendangan bebas yang
biasa dilakukan oleh pemain
sepakbola seperti David Beckham
termasuk gerak parabola?
30°
156. E7C4F=E;
?D
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Contoh 1.15
Tantangan
untuk Anda
Buktikan bahwa jika kecepatan
awalnya sama, pasangan sudut
elevasi yang hasil jumlahnya 90°
akan menghasilkan jarak terjauh
yang sama. Kemudian, apakah
waktu tempuh keduanya sama?
Untuk mencari nilai akar-akar dari y
= ax2 + bx + c digunakan rumus abc
berikut ini.
x1,2 =
2 4
2
a
157. Contoh 1.16 Kata Kunci
10 m
Analisis Gerak 19
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y v
P
yP
xP x
y v vy
vx
x
y
x
ay
ax
a
Gambar 1.17
Sebuah partikel bergerak melingkar.
(a) Posisi dan kecepatan partikel
pada saat tertentu.
(b) Komponen-komponen vektor
kecepatan.
(c) Percepatan gerak partikel dan
komponen-komponennya.
177. ?7?43:3D D753C3 G7=EAC ?7?43:3D D753C3 G7=EAC
Refleksi
22 Mudah dan Aktif Belajar Fisika untuk Kelas XI
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Peta Konsep
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Setelah mempelajari bab ini, Anda tentu dapat
membedakan antara besaran vektor dan besaran skalar
yang ada pada konsep gerak. Anda juga dapat
menentukan persamaan besaran fisika dari persamaan
yang diketahui dengan menggunakan operasi integral
dan diferensial. Dari materi bab ini, bagian manakah yang
Anda anggap sulit?
Dengan mempelajari bab ini, Anda dapat
menentukan bentuk lintasan gerak suatu benda. Pada
gerak parabola, titik terjauh dan titik tertinggi dapat
ditentukan dari persamaan gerak dan waktunya. Nah,
sekarang coba Anda sebutkan manfaat lain mempelajari
bab ini.
?7?43:3D
DF?4F- DF?4F-
B363 B363
