Download - X2 t06 02 resisted motion (2012)
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Resisted Motion
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Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
![Page 3: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/3.jpg)
Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)
![Page 4: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/4.jpg)
Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)Case 1 (horizontal line)
![Page 5: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/5.jpg)
Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)Case 1 (horizontal line)
![Page 6: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/6.jpg)
Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)Case 1 (horizontal line)
xm
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Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)Case 1 (horizontal line)
xm
R
![Page 8: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/8.jpg)
Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)Case 1 (horizontal line)
xm
R
Rxm
![Page 9: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/9.jpg)
Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)Case 1 (horizontal line)
xm
R
Rxm
mRx
![Page 10: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/10.jpg)
Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)Case 1 (horizontal line)
xm
R
Rxm
mRx
Case 2 (upwards motion)
![Page 11: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/11.jpg)
Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)Case 1 (horizontal line)
xm
R
Rxm
mRx
Case 2 (upwards motion)
![Page 12: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/12.jpg)
Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)Case 1 (horizontal line)
xm
R
Rxm
mRx
Case 2 (upwards motion)
xm
![Page 13: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/13.jpg)
Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)Case 1 (horizontal line)
xm
R
Rxm
mRx
Case 2 (upwards motion)
xm
mg
![Page 14: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/14.jpg)
Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)Case 1 (horizontal line)
xm
R
Rxm
mRx
Case 2 (upwards motion)
xm
Rmg
![Page 15: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/15.jpg)
Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)Case 1 (horizontal line)
xm
R
Rxm
mRx
Case 2 (upwards motion)
xm
R
Rmgxm
mg
![Page 16: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/16.jpg)
Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)Case 1 (horizontal line)
xm
R
Rxm
mRx
Case 2 (upwards motion)
xm
R
Rmgxm
mRgx
mg
![Page 17: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/17.jpg)
Resisted MotionResistance is ALWAYS in the OPPOSITE direction to the motion.
(Newton’s 3rd Law)Case 1 (horizontal line)
xm
R
Rxm
mRx
Case 2 (upwards motion)
xm
R
Rmgxm
mRgx
mg NOTE: greatest height still occurs when v = 0
![Page 18: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/18.jpg)
Case 3 (downwards motion)
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Case 3 (downwards motion)
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Case 3 (downwards motion)
xm
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Case 3 (downwards motion)
xm mg
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Case 3 (downwards motion)
xm
R
mg
![Page 23: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/23.jpg)
Case 3 (downwards motion)
xm
RRmgxm
mg
![Page 24: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/24.jpg)
Case 3 (downwards motion)
xm
RRmgxm
mRgx
mg
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Case 3 (downwards motion)
xm
RRmgxm
mRgx
mg NOTE:0when
occursvelocity terminalx
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Case 3 (downwards motion)
xm
RRmgxm
mRgx
mg NOTE:0when
occursvelocity terminalx
e.g. (i) A particle is projected vertically upwards with a velocity of u m/s in a resisting medium.Assuming that the retardation due to this resistance is equal tofind expressions for the greatest height reached and the time taken to reach that height.
2kv
![Page 27: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/27.jpg)
Case 3 (downwards motion)
xm
RRmgxm
mRgx
mg NOTE:0when
occursvelocity terminalx
e.g. (i) A particle is projected vertically upwards with a velocity of u m/s in a resisting medium.Assuming that the retardation due to this resistance is equal tofind expressions for the greatest height reached and the time taken to reach that height.
2kv
![Page 28: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/28.jpg)
Case 3 (downwards motion)
xm
RRmgxm
mRgx
mg NOTE:0when
occursvelocity terminalx
e.g. (i) A particle is projected vertically upwards with a velocity of u m/s in a resisting medium.Assuming that the retardation due to this resistance is equal tofind expressions for the greatest height reached and the time taken to reach that height.
2kv
xm
![Page 29: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/29.jpg)
Case 3 (downwards motion)
xm
RRmgxm
mRgx
mg NOTE:0when
occursvelocity terminalx
e.g. (i) A particle is projected vertically upwards with a velocity of u m/s in a resisting medium.Assuming that the retardation due to this resistance is equal tofind expressions for the greatest height reached and the time taken to reach that height.
2kv
xm
mg
![Page 30: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/30.jpg)
Case 3 (downwards motion)
xm
RRmgxm
mRgx
mg NOTE:0when
occursvelocity terminalx
e.g. (i) A particle is projected vertically upwards with a velocity of u m/s in a resisting medium.Assuming that the retardation due to this resistance is equal tofind expressions for the greatest height reached and the time taken to reach that height.
2kv
xm
mg 2kv
![Page 31: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/31.jpg)
Case 3 (downwards motion)
xm
RRmgxm
mRgx
mg NOTE:0when
occursvelocity terminalx
e.g. (i) A particle is projected vertically upwards with a velocity of u m/s in a resisting medium.Assuming that the retardation due to this resistance is equal tofind expressions for the greatest height reached and the time taken to reach that height.
2kv
xm
mg 2kv
uvx ,0
![Page 32: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/32.jpg)
Case 3 (downwards motion)
xm
RRmgxm
mRgx
mg NOTE:0when
occursvelocity terminalx
e.g. (i) A particle is projected vertically upwards with a velocity of u m/s in a resisting medium.Assuming that the retardation due to this resistance is equal tofind expressions for the greatest height reached and the time taken to reach that height.
2kv
xm
mg 2kv 2
2
vmkgx
kvmgxm
uvx ,0
![Page 33: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/33.jpg)
mkvmg
dxdvv
2
![Page 34: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/34.jpg)
mkvmg
dxdvv
2
2kvmgmv
dvdx
![Page 35: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/35.jpg)
mkvmg
dxdvv
2
2kvmgmv
dvdx
u
o
u
kvmgkvdv
km
kvmgvdvmx
02
2
22
![Page 36: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/36.jpg)
mkvmg
dxdvv
2
2kvmgmv
dvdx
u
o
u
kvmgkvdv
km
kvmgvdvmx
02
2
22
ukvmgk
m0
2log2
![Page 37: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/37.jpg)
mkvmg
dxdvv
2
2kvmgmv
dvdx
u
o
u
kvmgkvdv
km
kvmgvdvmx
02
2
22
ukvmgk
m0
2log2
mgku
km
mgkumg
km
mgkumgk
m
2
2
2
1log2
log2
loglog2
![Page 38: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/38.jpg)
mkvmg
dxdvv
2
2kvmgmv
dvdx
u
o
u
kvmgkvdv
km
kvmgvdvmx
02
2
22
ukvmgk
m0
2log2
mgku
km
mgkumg
km
mgkumgk
m
2
2
2
1log2
log2
loglog2
metres 1log2
is
height greatest the2
mgku
km
![Page 39: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/39.jpg)
2vmkgx
![Page 40: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/40.jpg)
2vmkgx
mkvmg
dtdv 2
![Page 41: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/41.jpg)
2vmkgx
mkvmg
dtdv 2
uu
vk
mgdv
km
kvmgdvmt
0 2
0
2
![Page 42: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/42.jpg)
2vmkgx
mkvmg
dtdv 2
uu
vk
mgdv
km
kvmgdvmt
0 2
0
2
u
vmgk
mgk
km
0
1tan
![Page 43: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/43.jpg)
2vmkgx
mkvmg
dtdv 2
uu
vk
mgdv
km
kvmgdvmt
0 2
0
2
u
vmgk
mgk
km
0
1tan
umgk
kgm
umgk
kgm
1
11
tan
0tantan
![Page 44: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/44.jpg)
2vmkgx
mkvmg
dtdv 2
uu
vk
mgdv
km
kvmgdvmt
0 2
0
2
u
vmgk
mgk
km
0
1tan
umgk
kgm
umgk
kgm
1
11
tan
0tantan
height.greatest reach the to
seconds tan it takes 1
u
mgk
kgm
![Page 45: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/45.jpg)
(ii) A body of mass 5kg is dropped from a height at which the gravitational acceleration is g.Assuming that air resistance is proportional to speed v, the constant of proportion being , find;
81
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(ii) A body of mass 5kg is dropped from a height at which the gravitational acceleration is g.Assuming that air resistance is proportional to speed v, the constant of proportion being , find;
81
a) the velocity after time t.
![Page 47: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/47.jpg)
(ii) A body of mass 5kg is dropped from a height at which the gravitational acceleration is g.Assuming that air resistance is proportional to speed v, the constant of proportion being , find;
81
a) the velocity after time t.
![Page 48: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/48.jpg)
(ii) A body of mass 5kg is dropped from a height at which the gravitational acceleration is g.Assuming that air resistance is proportional to speed v, the constant of proportion being , find;
81
a) the velocity after time t.
x5
![Page 49: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/49.jpg)
(ii) A body of mass 5kg is dropped from a height at which the gravitational acceleration is g.Assuming that air resistance is proportional to speed v, the constant of proportion being , find;
81
a) the velocity after time t.
x5 g5
![Page 50: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/50.jpg)
(ii) A body of mass 5kg is dropped from a height at which the gravitational acceleration is g.Assuming that air resistance is proportional to speed v, the constant of proportion being , find;
81
a) the velocity after time t.
x5 g5
v81
![Page 51: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/51.jpg)
(ii) A body of mass 5kg is dropped from a height at which the gravitational acceleration is g.Assuming that air resistance is proportional to speed v, the constant of proportion being , find;
81
a) the velocity after time t.
x5 g5
v81 vgx
vgx
4018155
![Page 52: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/52.jpg)
(ii) A body of mass 5kg is dropped from a height at which the gravitational acceleration is g.Assuming that air resistance is proportional to speed v, the constant of proportion being , find;
81
a) the velocity after time t.
x5 g5
v81 vgx
vgx
4018155
4040 vg
dtdv
![Page 53: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/53.jpg)
(ii) A body of mass 5kg is dropped from a height at which the gravitational acceleration is g.Assuming that air resistance is proportional to speed v, the constant of proportion being , find;
81
a) the velocity after time t.
x5 g5
v81 vgx
vgx
4018155
4040 vg
dtdv
v
vgdvt
0 4040
![Page 54: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/54.jpg)
(ii) A body of mass 5kg is dropped from a height at which the gravitational acceleration is g.Assuming that air resistance is proportional to speed v, the constant of proportion being , find;
81
a) the velocity after time t.
x5 g5
v81 vgx
vgx
4018155
4040 vg
dtdv
v
vgdvt
0 4040
vgg
gvgvg v
4040log40
40log40log4040log40 0
![Page 55: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/55.jpg)
vg
gt40
40log40
![Page 56: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/56.jpg)
vg
gt40
40log40
40
4040 t
evg
g
![Page 57: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/57.jpg)
vg
gt40
40log40
40
4040 t
evg
g
40
4040 t
eg
vg
![Page 58: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/58.jpg)
vg
gt40
40log40
40
4040 t
evg
g
40
4040 t
eg
vg
40
40
40
140
4040
4040
t
t
t
egv
gegv
gevg
![Page 59: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/59.jpg)
vg
gt40
40log40
40
4040 t
evg
g
40
4040 t
eg
vg
40
40
40
140
4040
4040
t
t
t
egv
gegv
gevg
b) the terminal velocity
![Page 60: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/60.jpg)
vg
gt40
40log40
40
4040 t
evg
g
40
4040 t
eg
vg
40
40
40
140
4040
4040
t
t
t
egv
gegv
gevg
b) the terminal velocity0when occurs velocity terminal x
![Page 61: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/61.jpg)
vg
gt40
40log40
40
4040 t
evg
g
40
4040 t
eg
vg
40
40
40
140
4040
4040
t
t
t
egv
gegv
gevg
b) the terminal velocity0when occurs velocity terminal x
gv
vg
404010i.e.
![Page 62: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/62.jpg)
vg
gt40
40log40
40
4040 t
evg
g
40
4040 t
eg
vg
40
40
40
140
4040
4040
t
t
t
egv
gegv
gevg
b) the terminal velocity0when occurs velocity terminal x
gv
vg
404010i.e.
OR
![Page 63: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/63.jpg)
vg
gt40
40log40
40
4040 t
evg
g
40
4040 t
eg
vg
40
40
40
140
4040
4040
t
t
t
egv
gegv
gevg
b) the terminal velocity0when occurs velocity terminal x
gv
vg
404010i.e.
OR
g
egvt
tt
40
140limlim 40
![Page 64: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/64.jpg)
vg
gt40
40log40
40
4040 t
evg
g
40
4040 t
eg
vg
40
40
40
140
4040
4040
t
t
t
egv
gegv
gevg
b) the terminal velocity0when occurs velocity terminal x
gv
vg
404010i.e.
OR
g
egvt
tt
40
140limlim 40
m/s40isvelocity terminal g
![Page 65: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/65.jpg)
c) The distance it has fallen after time t
![Page 66: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/66.jpg)
c) The distance it has fallen after time t
40140t
egdtdx
![Page 67: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/67.jpg)
c) The distance it has fallen after time t
40140t
egdtdx
t t
dtegx0
40140
![Page 68: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/68.jpg)
c) The distance it has fallen after time t
40140t
egdtdx
t t
dtegx0
40140
tt
etgx0
404040
![Page 69: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/69.jpg)
c) The distance it has fallen after time t
40140t
egdtdx
t t
dtegx0
40140
tt
etgx0
404040
ggegtx
etgx
t
t
1600160040
4004040
40
40
![Page 70: X2 t06 02 resisted motion (2012)](https://reader034.vdocuments.site/reader034/viewer/2022042813/54c461d84a795932068b467d/html5/thumbnails/70.jpg)
c) The distance it has fallen after time t
40140t
egdtdx
t t
dtegx0
40140
tt
etgx0
404040
ggegtx
etgx
t
t
1600160040
4004040
40
40
Exercise 8C; 2, 4, 5, 6, 8, 10, 13, 16