Upload
nigel-simmons
View
516
Download
1
Embed Size (px)
Citation preview
Projectile Motion
Projectile Motiony
x
Projectile Motiony
x
v m/s
Projectile Motiony
x
v m/s
Projectile Motiony
x
v m/s
45rangemaximum
Initial conditions
Projectile Motiony
x
v m/s
45rangemaximum
Initial conditions when t = 0
v
Projectile Motiony
x
v m/s
45rangemaximum
Initial conditions when t = 0
v
x
y
Projectile Motiony
x
v m/s
45rangemaximum
Initial conditions when t = 0
v
x
y
cos
cos
vxvx
Projectile Motiony
x
v m/s
45rangemaximum
Initial conditions when t = 0
v
x
y
cos
cos
vxvx
sin
sin
vyvy
Projectile Motiony
x
v m/s
45rangemaximum
Initial conditions when t = 0
v
x
y
cos
cos
vxvx
sin
sin
vyvy
0x
Projectile Motiony
x
v m/s
45rangemaximum
Initial conditions when t = 0
v
x
y
cos
cos
vxvx
sin
sin
vyvy
0x 0y
0x gy
0x gy
1cx
0x gy
1cx 2cgty
0x gy
1cx 2cgty sin cos0,when vyvxt
0x gy
1cx 2cgty sin cos0,when vyvxt
coscos1
vxvc
0x gy
1cx 2cgty sin cos0,when vyvxt
coscos1
vxvc
sin
sin2
vgtyvc
0x gy
1cx 2cgty sin cos0,when vyvxt
coscos1
vxvc
sin
sin2
vgtyvc
3cos cvtx 42 sin
21 cvtgty
0x gy
1cx 2cgty sin cos0,when vyvxt
coscos1
vxvc
sin
sin2
vgtyvc
3cos cvtx 42 sin
21 cvtgty
0 00,when yxt
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
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
Common Questions
Common Questions
(1) When does the particle hit the ground?
Common Questions
(1) When does the particle hit the ground?0when ground thehits Particle y
Common Questions
(1) When does the particle hit the ground?0when ground thehits Particle y
(2) What is the range of the particle?
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
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
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?
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
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
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?
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
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
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
Summary
SummaryA particle undergoing projectile motion obeys
SummaryA particle undergoing projectile motion obeys
0x gy and
SummaryA particle undergoing projectile motion obeys
0x gy and
with initial conditions
SummaryA particle undergoing projectile motion obeys
0x gy and
with initial conditions
cosvx sinvy and
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
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
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
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
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
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
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
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
0x 10y
0x 10y
1cx
0x 10y
1cx 210 cty
0x 10y
1cx 210 cty 15 200,when yxt
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
320 ctx
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
320 ctx 42 155 ctty
0x 10y
1cx 210 cty 15 200,when yxt
20201
xc 1510
152
tyc
320 ctx 42 155 ctty 0 00,when yxt
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
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
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
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
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
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
b) range
b) range
time of flight is 3 seconds
b) range
time of flight is 3 seconds
06 320,3when
xt
b) range
time of flight is 3 seconds
06 320,3when
xt
60m is range
b) range
time of flight is 3 seconds
06 320,3when
xt
60m is range
second21after ball theofdirection and velocity c)
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
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
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
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
d) cartesian equation of the path
d) cartesian equation of the path
20
20xt
tx
d) cartesian equation of the path
20
20xt
tx
43
80
2015
205
155
2
2
2
xxy
xxy
tty
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