12 x1 t07 01 projectile motion (2013)
TRANSCRIPT
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Projectile Motion
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Projectile Motiony
x
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Projectile Motiony
x
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Projectile Motiony
x
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Projectile Motiony
x
45rangemaximum
Initial conditions
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Projectile Motiony
x
45rangemaximum
Initial conditions when t = 0
v
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Projectile Motiony
x
45rangemaximum
Initial conditions when t = 0
v
x
y
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Projectile Motiony
x
45rangemaximum
Initial conditions when t = 0
v
x
y
cos
cos
vxvx
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Projectile Motiony
x
45rangemaximum
Initial conditions when t = 0
v
x
y
cos
cos
vxvx
sin
sin
vyvy
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Projectile Motiony
x
45rangemaximum
Initial conditions when t = 0
v
x
y
cos
cos
vxvx
sin
sin
vyvy
0x
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Projectile Motiony
x
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
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0x gy
1cx 2cgty sin cos0,when vyvxt
coscos1
vxvc
sin
sin2
vgtyvc
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0x gy
1cx 2cgty sin cos0,when vyvxt
coscos1
vxvc
sin
sin2
vgtyvc
3cos cvtx 42 sin
21 cvtgty
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0x gy
1cx 2cgty sin cos0,when vyvxt
coscos1
vxvc
sin
sin2
vgtyvc
3cos cvtx 42 sin
21 cvtgty
0 00,when yxt
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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
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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
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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
Note: parametric coordinates of a parabola
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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
Note: parametric coordinates of a parabola
cosxt
v
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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
Note: parametric coordinates of a parabola
cosxt
v
2
2 2
sin2 cos cos
gx xyv
22
2 sec tan2gxy xv
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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
Note: parametric coordinates of a parabola
cosxt
v
2
2 2
sin2 cos cos
gx xyv
22
2 sec tan2gxy xv
2
22 tan 1 tan
2gxy xv
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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 intosubstituteroots of the quadratic
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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?
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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?
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(3) What is the greatest height of the particle?
0 when find yi yii intosubstitute
![Page 36: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/36.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
roots of the quadratic
vertex of the parabola
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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?
0 when find yi yii intosubstitute
(4) What angle does the particle make with the ground?
![Page 38: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/38.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 39: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/39.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 40: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/40.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
![Page 41: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/41.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
roots of the quadratic
vertex of the parabola
(i) find slope of the tangent tanii m
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Summary
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SummaryA particle undergoing projectile motion obeys
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SummaryA particle undergoing projectile motion obeys
0x gy and
![Page 45: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/45.jpg)
SummaryA particle undergoing projectile motion obeys
0x gy and
with initial conditions
![Page 46: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/46.jpg)
SummaryA particle undergoing projectile motion obeys
0x gy and
with initial conditions
cosvx sinvy and
![Page 47: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/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
![Page 48: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/48.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 49: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/49.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 50: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/50.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 51: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/51.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 52: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/52.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 53: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/53.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 54: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/54.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 55: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/55.jpg)
0x 10y
![Page 56: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/56.jpg)
0x 10y
1cx
![Page 57: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/57.jpg)
0x 10y
1cx 210 cty
![Page 58: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/58.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
![Page 59: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/59.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc
![Page 60: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/60.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
![Page 61: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/61.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
320 ctx
![Page 62: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/62.jpg)
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
320 ctx 42 155 ctty
![Page 63: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/63.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 64: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/64.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 65: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/65.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 66: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/66.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 67: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/67.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 68: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/68.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 69: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/69.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 70: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/70.jpg)
b) range
![Page 71: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/71.jpg)
b) range
time of flight is 3 seconds
![Page 72: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/72.jpg)
b) range
time of flight is 3 seconds
06 320,3when
xt
![Page 73: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/73.jpg)
b) range
time of flight is 3 seconds
06 320,3when
xt
60m is range
![Page 74: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/74.jpg)
b) range
time of flight is 3 seconds
06 320,3when
xt
60m is range
second21after ball theofdirection and velocity c)
![Page 75: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/75.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
![Page 76: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/76.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 77: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/77.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
![Page 78: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/78.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
horizontal the to4326 of anglean
at travelingisit and m/s510 velocity second,21after
![Page 79: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/79.jpg)
d) cartesian equation of the path
![Page 80: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/80.jpg)
d) cartesian equation of the path
20
20xt
tx
![Page 81: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/81.jpg)
d) cartesian equation of the path
20
20xt
tx
43
80
2015
205
155
2
2
2
xxy
xxy
tty
![Page 82: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/82.jpg)
d) cartesian equation of the path
20
20xt
tx
43
80
2015
205
155
2
2
2
xxy
xxy
tty
![Page 83: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/83.jpg)
d) cartesian equation of the path
20
20xt
tx
43
80
2015
205
155
2
2
2
xxy
xxy
tty
![Page 84: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/84.jpg)
d) cartesian equation of the path
20
20xt
tx
43
80
2015
205
155
2
2
2
xxy
xxy
tty
Using the cartesian equation to solve the problem
![Page 85: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/85.jpg)
d) cartesian equation of the path
20
20xt
tx
43
80
2015
205
155
2
2
2
xxy
xxy
tty
Using the cartesian equation to solve the problem
a) greatest height is y value of the vertex
![Page 86: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/86.jpg)
d) cartesian equation of the path
20
20xt
tx
43
80
2015
205
155
2
2
2
xxy
xxy
tty
Using the cartesian equation to solve the problem
a) greatest height is y value of the vertex23 14( )(0)
4 809
16
![Page 87: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/87.jpg)
d) cartesian equation of the path
20
20xt
tx
43
80
2015
205
155
2
2
2
xxy
xxy
tty
Using the cartesian equation to solve the problem
a) greatest height is y value of the vertex23 14( )(0)
4 809
16
49 20
16 1454
ya
![Page 88: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/88.jpg)
d) cartesian equation of the path
20
20xt
tx
43
80
2015
205
155
2
2
2
xxy
xxy
tty
Using the cartesian equation to solve the problem
a) greatest height is y value of the vertex23 14( )(0)
4 809
16
49 20
16 1454
ya
ground theabove m4111 isheight greatest
![Page 89: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/89.jpg)
b) range
![Page 90: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/90.jpg)
b) range2 3
80 4
34 20
x xy
x x
![Page 91: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/91.jpg)
b) range2 3
80 4
34 20
x xy
x x
roots are 0 and 6060m isrange
![Page 92: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/92.jpg)
b) range2 3
80 4
34 20
x xy
x x
roots are 0 and 6060m isrange
second21after ball theofdirection and velocity c)
![Page 93: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/93.jpg)
b) range2 3
80 4
34 20
x xy
x x
roots are 0 and 6060m isrange
second21after ball theofdirection and velocity c)
1when , 102
t x
![Page 94: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/94.jpg)
b) range2 3
80 4
34 20
x xy
x x
roots are 0 and 6060m isrange
second21after ball theofdirection and velocity c)
1when , 102
t x 2 380 4
340 4
x xy
dy xdx
![Page 95: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/95.jpg)
b) range2 3
80 4
34 20
x xy
x x
roots are 0 and 6060m isrange
second21after ball theofdirection and velocity c)
1when , 102
t x 2 380 4
340 4
x xy
dy xdx
1when 10,2
dyxdx
![Page 96: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/96.jpg)
b) range2 3
80 4
34 20
x xy
x x
roots are 0 and 6060m isrange
second21after ball theofdirection and velocity c)
1when , 102
t x 2 380 4
340 4
x xy
dy xdx
1when 10,2
dyxdx
432621tan
![Page 97: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/97.jpg)
b) range2 3
80 4
34 20
x xy
x x
roots are 0 and 6060m isrange
second21after ball theofdirection and velocity c)
1when , 102
t x 2 380 4
340 4
x xy
dy xdx
1when 10,2
dyxdx
432621tan
cosxv
t
![Page 98: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/98.jpg)
b) range2 3
80 4
34 20
x xy
x x
roots are 0 and 6060m isrange
second21after ball theofdirection and velocity c)
1when , 102
t x 2 380 4
340 4
x xy
dy xdx
1when 10,2
dyxdx
432621tan
cosxv
t
2
15
![Page 99: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/99.jpg)
b) range2 3
80 4
34 20
x xy
x x
roots are 0 and 6060m isrange
second21after ball theofdirection and velocity c)
1when , 102
t x 2 380 4
340 4
x xy
dy xdx
1when 10,2
dyxdx
432621tan
cosxv
t
2
15
101 22 5
10 5
![Page 100: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/100.jpg)
b) range2 3
80 4
34 20
x xy
x x
roots are 0 and 6060m isrange
second21after ball theofdirection and velocity c)
1when , 102
t x 2 380 4
340 4
x xy
dy xdx
1when 10,2
dyxdx
432621tan
cosxv
t
2
15
101 22 5
10 5
1after second, velocity 10 5m/s and it is2
traveling at an angle of 26 34 to the horizontal
![Page 101: 12 x1 t07 01 projectile motion (2013)](https://reader034.vdocument.in/reader034/viewer/2022042701/55aa56461a28ab9d768b4878/html5/thumbnails/101.jpg)
Exercise 3G; 1ac, 2ac, 4, 6, 8, 9, 11, 13, 16, 18
Exercise 3H; 2, 4, 6, 7, 10, 11
b) range2 3
80 4
34 20
x xy
x x
roots are 0 and 6060m isrange
second21after ball theofdirection and velocity c)
1when , 102
t x 2 380 4
340 4
x xy
dy xdx
1when 10,2
dyxdx
432621tan
cosxv
t
2
15
101 22 5
10 5
1after second, velocity 10 5m/s and it is2
traveling at an angle of 26 34 to the horizontal