12x1 t07 01 projectile motion (2011)

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