12x1 t07 03 projectile motion (2010)
TRANSCRIPT
![Page 1: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/1.jpg)
Projectile Motion
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Projectile Motiony
x
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Projectile Motiony
x
v m/s
![Page 4: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/4.jpg)
Projectile Motiony
x
v m/s
![Page 5: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/5.jpg)
Projectile Motiony
x
v m/s
45rangemaximum
Initial conditions
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Projectile Motiony
x
v m/s
45rangemaximum
Initial conditions when t = 0
v
![Page 7: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/7.jpg)
Projectile Motiony
x
v m/s
45rangemaximum
Initial conditions when t = 0
v
x
y
![Page 8: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/8.jpg)
Projectile Motiony
x
v m/s
45rangemaximum
Initial conditions when t = 0
v
x
y
cos
cos
vxvx
![Page 9: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/9.jpg)
Projectile Motiony
x
v m/s
45rangemaximum
Initial conditions when t = 0
v
x
y
cos
cos
vxvx
sin
sin
vyvy
![Page 10: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/10.jpg)
Projectile Motiony
x
v m/s
45rangemaximum
Initial conditions when t = 0
v
x
y
cos
cos
vxvx
sin
sin
vyvy
0x
![Page 11: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/11.jpg)
Projectile Motiony
x
v m/s
45rangemaximum
Initial conditions when t = 0
v
x
y
cos
cos
vxvx
sin
sin
vyvy
0x 0y
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0x gy
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0x gy
1cx
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0x gy
1cx 2cgty
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0x gy
1cx 2cgty sin cos0,when vyvxt
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0x gy
1cx 2cgty sin cos0,when vyvxt
coscos1
vxvc
![Page 17: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/17.jpg)
0x gy
1cx 2cgty sin cos0,when vyvxt
coscos1
vxvc
sin
sin2
vgtyvc
![Page 18: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/18.jpg)
0x gy
1cx 2cgty sin cos0,when vyvxt
coscos1
vxvc
sin
sin2
vgtyvc
3cos cvtx 42 sin
21 cvtgty
![Page 19: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/19.jpg)
0x gy
1cx 2cgty sin cos0,when vyvxt
coscos1
vxvc
sin
sin2
vgtyvc
3cos cvtx 42 sin
21 cvtgty
0 00,when yxt
![Page 20: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/20.jpg)
0x gy
1cx 2cgty sin cos0,when vyvxt
coscos1
vxvc
sin
sin2
vgtyvc
3cos cvtx 42 sin
21 cvtgty
0 00,when yxt
cos03
vtxc
![Page 21: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/21.jpg)
0x gy
1cx 2cgty sin cos0,when vyvxt
coscos1
vxvc
sin
sin2
vgtyvc
3cos cvtx 42 sin
21 cvtgty
0 00,when yxt
cos03
vtxc
sin21
0
2
4
vtgty
c
![Page 22: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/22.jpg)
Common Questions
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Common Questions
(1) When does the particle hit the ground?
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Common Questions
(1) When does the particle hit the ground?0when ground thehits Particle y
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Common Questions
(1) When does the particle hit the ground?0when ground thehits Particle y
(2) What is the range of the particle?
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Common Questions
(1) When does the particle hit the ground?0when ground thehits Particle y
(2) What is the range of the particle? 0 when find yi
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Common Questions
(1) When does the particle hit the ground?0when ground thehits Particle y
(2) What is the range of the particle? 0 when find yi
xii intosubstitute
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Common Questions
(1) When does the particle hit the ground?0when ground thehits Particle y
(2) What is the range of the particle? 0 when find yi
xii intosubstitute(3) What is the greatest height of the particle?
![Page 29: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/29.jpg)
Common Questions
(1) When does the particle hit the ground?0when ground thehits Particle y
(2) What is the range of the particle? 0 when find yi
xii intosubstitute(3) What is the greatest height of the particle?
0 when find yi
![Page 30: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/30.jpg)
Common Questions
(1) When does the particle hit the ground?0when ground thehits Particle y
(2) What is the range of the particle? 0 when find yi
xii intosubstitute(3) What is the greatest height of the particle?
0 when find yi yii intosubstitute
![Page 31: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/31.jpg)
Common Questions
(1) When does the particle hit the ground?0when ground thehits Particle y
(2) What is the range of the particle? 0 when find yi
xii intosubstitute(3) What is the greatest height of the particle?
0 when find yi yii intosubstitute
(4) What angle does the particle make with the ground?
![Page 32: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/32.jpg)
Common Questions
(1) When does the particle hit the ground?0when ground thehits Particle y
(2) What is the range of the particle? 0 when find yi
xii intosubstitute(3) What is the greatest height of the particle?
0 when find yi yii intosubstitute
(4) What angle does the particle make with the ground? 0 when find yi
![Page 33: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/33.jpg)
Common Questions
(1) When does the particle hit the ground?0when ground thehits Particle y
(2) What is the range of the particle? 0 when find yi
xii intosubstitute(3) What is the greatest height of the particle?
0 when find yi yii intosubstitute
(4) What angle does the particle make with the ground? 0 when find yi
yii intosubstitute
![Page 34: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/34.jpg)
Common Questions
(1) When does the particle hit the ground?0when ground thehits Particle y
(2) What is the range of the particle? 0 when find yi
xii intosubstitute(3) What is the greatest height of the particle?
0 when find yi yii intosubstitute
(4) What angle does the particle make with the ground? 0 when find yi
yii intosubstitute
xyiii tan
x
y
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Summary
![Page 36: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/36.jpg)
SummaryA particle undergoing projectile motion obeys
![Page 37: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/37.jpg)
SummaryA particle undergoing projectile motion obeys
0x gy and
![Page 38: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/38.jpg)
SummaryA particle undergoing projectile motion obeys
0x gy and
with initial conditions
![Page 39: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/39.jpg)
SummaryA particle undergoing projectile motion obeys
0x gy and
with initial conditions
cosvx sinvy and
![Page 40: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/40.jpg)
SummaryA particle undergoing projectile motion obeys
0x gy and
with initial conditions
cosvx sinvy and
e.g. A ball is thrown with an initial velocity of 25 m/s at an angle ofto the ground. Determine;.
43tan 1
![Page 41: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/41.jpg)
SummaryA particle undergoing projectile motion obeys
0x gy and
with initial conditions
cosvx sinvy and
e.g. A ball is thrown with an initial velocity of 25 m/s at an angle ofto the ground. Determine;.
43tan 1
a) greatest height obtained
![Page 42: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/42.jpg)
SummaryA particle undergoing projectile motion obeys
0x gy and
with initial conditions
cosvx sinvy and
e.g. A ball is thrown with an initial velocity of 25 m/s at an angle ofto the ground. Determine;.
43tan 1
Initial conditionsa) greatest height obtained
![Page 43: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/43.jpg)
SummaryA particle undergoing projectile motion obeys
0x gy and
with initial conditions
cosvx sinvy and
e.g. A ball is thrown with an initial velocity of 25 m/s at an angle ofto the ground. Determine;.
43tan 1
Initial conditionsa) greatest height obtained
43tan 1
3
4
5
![Page 44: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/44.jpg)
SummaryA particle undergoing projectile motion obeys
0x gy and
with initial conditions
cosvx sinvy and
e.g. A ball is thrown with an initial velocity of 25 m/s at an angle ofto the ground. Determine;.
43tan 1
Initial conditionsa) greatest height obtained
43tan 1
3
4
5cosvx
![Page 45: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/45.jpg)
SummaryA particle undergoing projectile motion obeys
0x gy and
with initial conditions
cosvx sinvy and
e.g. A ball is thrown with an initial velocity of 25 m/s at an angle ofto the ground. Determine;.
43tan 1
Initial conditionsa) greatest height obtained
43tan 1
3
4
5
m/s205425
x
cosvx
![Page 46: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/46.jpg)
SummaryA particle undergoing projectile motion obeys
0x gy and
with initial conditions
cosvx sinvy and
e.g. A ball is thrown with an initial velocity of 25 m/s at an angle ofto the ground. Determine;.
43tan 1
Initial conditionsa) greatest height obtained
43tan 1
3
4
5
m/s205425
x
sinvy cosvx
![Page 47: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/47.jpg)
SummaryA particle undergoing projectile motion obeys
0x gy and
with initial conditions
cosvx sinvy and
e.g. A ball is thrown with an initial velocity of 25 m/s at an angle ofto the ground. Determine;.
43tan 1
Initial conditionsa) greatest height obtained
43tan 1
3
4
5
m/s205425
x
sinvy cosvx
m/s155325
y
![Page 48: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/48.jpg)
0x 10y
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0x 10y
1cx
![Page 50: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/50.jpg)
0x 10y
1cx 210 cty
![Page 51: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/51.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
![Page 52: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/52.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc
![Page 53: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/53.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
![Page 54: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/54.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
320 ctx
![Page 55: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/55.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
320 ctx 42 155 ctty
![Page 56: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/56.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
320 ctx 42 155 ctty 0 00,when yxt
![Page 57: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/57.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
320 ctx 42 155 ctty 0 00,when yxt
txc
2003
![Page 58: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/58.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
320 ctx 42 155 ctty 0 00,when yxt
txc
2003
tty
c
155
02
4
![Page 59: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/59.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
320 ctx 42 155 ctty 0 00,when yxt
txc
2003
tty
c
155
02
4
0when occursheight greatest y
![Page 60: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/60.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
320 ctx 42 155 ctty 0 00,when yxt
txc
2003
tty
c
155
02
4
0when occursheight greatest y
23
01510
t
t
![Page 61: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/61.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
320 ctx 42 155 ctty 0 00,when yxt
txc
2003
tty
c
155
02
4
0when occursheight greatest y
23
01510
t
t
445
2315
235,
23when
2
yt
![Page 62: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/62.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
320 ctx 42 155 ctty 0 00,when yxt
txc
2003
tty
c
155
02
4
0when occursheight greatest y
23
01510
t
t
445
2315
235,
23when
2
yt
ground theabove m4111 isheight greatest
![Page 63: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/63.jpg)
b) range
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b) range
time of flight is 3 seconds
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b) range
time of flight is 3 seconds
06 320,3when
xt
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b) range
time of flight is 3 seconds
06 320,3when
xt
60m is range
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b) range
time of flight is 3 seconds
06 320,3when
xt
60m is range
second21after ball theofdirection and velocity c)
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b) range
time of flight is 3 seconds
06 320,3when
xt
60m is range
second21after ball theofdirection and velocity c)
01
152110 20,
21when
yxt
![Page 69: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/69.jpg)
b) range
time of flight is 3 seconds
06 320,3when
xt
60m is range
second21after ball theofdirection and velocity c)
01
152110 20,
21when
yxt
20
10510
![Page 70: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/70.jpg)
b) range
time of flight is 3 seconds
06 320,3when
xt
60m is range
second21after ball theofdirection and velocity c)
01
152110 20,
21when
yxt
20
10510
432621tan
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b) range
time of flight is 3 seconds
06 320,3when
xt
60m is range
second21after ball theofdirection and velocity c)
01
152110 20,
21when
yxt
20
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432621tan
horizontal the to4326 of anglean
at travelingisit and m/s510 velocity second,21after
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d) cartesian equation of the path
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d) cartesian equation of the path
20
20xt
tx
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d) cartesian equation of the path
20
20xt
tx
43
80
2015
205
155
2
2
2
xxy
xxy
tty
![Page 75: 12X1 T07 03 projectile motion (2010)](https://reader034.vdocuments.net/reader034/viewer/2022052705/5880f2e71a28abc3368b4d4b/html5/thumbnails/75.jpg)
d) cartesian equation of the path
20
20xt
tx
43
80
2015
205
155
2
2
2
xxy
xxy
tty
Exercise 3G; 1ac, 2ac, 4, 6, 8, 9, 11, 13, 16, 18
Exercise 3H; 2, 4, 6, 7, 10, 11