12x1 t07 01 projectile motion (2011)

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Projectile Motion

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Page 1: 12X1 T07 01 projectile motion (2011)

Projectile Motion

Page 2: 12X1 T07 01 projectile motion (2011)

Projectile Motiony

x

Page 3: 12X1 T07 01 projectile motion (2011)

Projectile Motiony

x

v m/s

Page 4: 12X1 T07 01 projectile motion (2011)

Projectile Motiony

x

v m/s

Page 5: 12X1 T07 01 projectile motion (2011)

Projectile Motiony

x

v m/s

45rangemaximum

Initial conditions

Page 6: 12X1 T07 01 projectile motion (2011)

Projectile Motiony

x

v m/s

45rangemaximum

Initial conditions when t = 0

v

Page 7: 12X1 T07 01 projectile motion (2011)

Projectile Motiony

x

v m/s

45rangemaximum

Initial conditions when t = 0

v

x

y

Page 8: 12X1 T07 01 projectile motion (2011)

Projectile Motiony

x

v m/s

45rangemaximum

Initial conditions when t = 0

v

x

y

cos

cos

vxvx

Page 9: 12X1 T07 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

Projectile Motiony

x

v m/s

45rangemaximum

Initial conditions when t = 0

v

x

y

cos

cos

vxvx

sin

sin

vyvy

0x 0y

Page 12: 12X1 T07 01 projectile motion (2011)

0x gy

Page 13: 12X1 T07 01 projectile motion (2011)

0x gy

1cx

Page 14: 12X1 T07 01 projectile motion (2011)

0x gy

1cx 2cgty

Page 15: 12X1 T07 01 projectile motion (2011)

0x gy

1cx 2cgty sin cos0,when vyvxt

Page 16: 12X1 T07 01 projectile motion (2011)

0x gy

1cx 2cgty sin cos0,when vyvxt

coscos1

vxvc

Page 17: 12X1 T07 01 projectile motion (2011)

0x gy

1cx 2cgty sin cos0,when vyvxt

coscos1

vxvc

sin

sin2

vgtyvc

Page 18: 12X1 T07 01 projectile motion (2011)

0x gy

1cx 2cgty sin cos0,when vyvxt

coscos1

vxvc

sin

sin2

vgtyvc

3cos cvtx 42 sin

21 cvtgty

Page 19: 12X1 T07 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

Common Questions

Page 23: 12X1 T07 01 projectile motion (2011)

Common Questions

(1) When does the particle hit the ground?

Page 24: 12X1 T07 01 projectile motion (2011)

Common Questions

(1) When does the particle hit the ground?0when ground thehits Particle y

Page 25: 12X1 T07 01 projectile motion (2011)

Common Questions

(1) When does the particle hit the ground?0when ground thehits Particle y

(2) What is the range of the particle?

Page 26: 12X1 T07 01 projectile motion (2011)

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

Page 27: 12X1 T07 01 projectile motion (2011)

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

Page 28: 12X1 T07 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 35: 12X1 T07 01 projectile motion (2011)

Summary

Page 36: 12X1 T07 01 projectile motion (2011)

SummaryA particle undergoing projectile motion obeys

Page 37: 12X1 T07 01 projectile motion (2011)

SummaryA particle undergoing projectile motion obeys

0x gy and

Page 38: 12X1 T07 01 projectile motion (2011)

SummaryA particle undergoing projectile motion obeys

0x gy and

with initial conditions

Page 39: 12X1 T07 01 projectile motion (2011)

SummaryA particle undergoing projectile motion obeys

0x gy and

with initial conditions

cosvx sinvy and

Page 40: 12X1 T07 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

0x 10y

Page 49: 12X1 T07 01 projectile motion (2011)

0x 10y

1cx

Page 50: 12X1 T07 01 projectile motion (2011)

0x 10y

1cx 210 cty

Page 51: 12X1 T07 01 projectile motion (2011)

0x 10y

1cx 210 cty 15 200,when yxt

Page 52: 12X1 T07 01 projectile motion (2011)

0x 10y

1cx 210 cty 15 200,when yxt

20201

xc

Page 53: 12X1 T07 01 projectile motion (2011)

0x 10y

1cx 210 cty 15 200,when yxt

20201

xc 1510

152

tyc

Page 54: 12X1 T07 01 projectile motion (2011)

0x 10y

1cx 210 cty 15 200,when yxt

20201

xc 1510

152

tyc

320 ctx

Page 55: 12X1 T07 01 projectile motion (2011)

0x 10y

1cx 210 cty 15 200,when yxt

20201

xc 1510

152

tyc

320 ctx 42 155 ctty

Page 56: 12X1 T07 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

b) range

Page 64: 12X1 T07 01 projectile motion (2011)

b) range

time of flight is 3 seconds

Page 65: 12X1 T07 01 projectile motion (2011)

b) range

time of flight is 3 seconds

06 320,3when

xt

Page 66: 12X1 T07 01 projectile motion (2011)

b) range

time of flight is 3 seconds

06 320,3when

xt

60m is range

Page 67: 12X1 T07 01 projectile motion (2011)

b) range

time of flight is 3 seconds

06 320,3when

xt

60m is range

second21after ball theofdirection and velocity c)

Page 68: 12X1 T07 01 projectile motion (2011)

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 01 projectile motion (2011)

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 01 projectile motion (2011)

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 71: 12X1 T07 01 projectile motion (2011)

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 72: 12X1 T07 01 projectile motion (2011)

d) cartesian equation of the path

Page 73: 12X1 T07 01 projectile motion (2011)

d) cartesian equation of the path

20

20xt

tx

Page 74: 12X1 T07 01 projectile motion (2011)

d) cartesian equation of the path

20

20xt

tx

43

80

2015

205

155

2

2

2

xxy

xxy

tty

Page 75: 12X1 T07 01 projectile motion (2011)

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