Maths

1. Project Missile Trajectory
“North Korea claims it fired a Hwasong-14 missile which reached an altitude of 2,802 kilometres and
flew 933km in 39 minutes.
David Wright, co-director of the Global Security Program at the US-based Union of Concerned Scientists, said
the missile was fired at a "very highly lofted trajectory".
If the missile had been fired at a standard trajectory, he said it could have a maximum range of 6,700km.”
(ABC NEWS)
North Korea- Japan =1043km
North Korea- Guam=3430km
North Korea- Adelaide=8441km
The recent events of missile firefrom North Korehave been frightening. This assignment is
not intended to frighten nor to make light of the issue, but explorethe mathematics of
missile arcs.
Figure 1: ABC News (2017)WherecouldaNorthKoreanintercontinentalballisticmissilehit?Accessed14/09/17
Introduction:

2. All calculations are representing 1000s of Kms
A
1. Draw the missile launchof y=5X
2. What is the y intercept. What does the y intercept represent?
3. What is the x intercept. What doesthe x intercept represent?
4. Why is thisan unrealistic equationfor a missile launch?
B
1. Draw the missile launchof y=x2
+3
2. Use algebra to find the y intercept. What doesthe y intercept represent?
3. Use algebra to find the x intercept. What doesthe x intercept represent?
4. Discussthe coordinatesof the vertex. Whatdoes thisrepresent?
5. Why is thisan unrealistic equationfor a missile launch?
C
1. Draw the missile launchof y=(x-2)2
+3
2. Use algebra to find the y intercept. What doesthe y intercept represent?
3. Use algebra to find the x intercept. What doesthe x intercept represent?
4. Discussthe coordinatesof the vertex. Whatdoes thisrepresent?
5. Why is thisan unrealistic equationfor a missile launch?

3. D
1. Draw the missile launchof y=-(x-2)2
-3
2. Use algebra to find the y intercept. What doesthe y intercept represent?
3. Use algebra to find the x intercept. What doesthe x intercept represent?
4. Discussthe coordinatesof the vertex. Whatdoes thisrepresent?
5. Why is this an unrealistic equationfor a missile launch?
E
1. Draw the missile launchof y=-2(x+1)(x-2)
2. Use algebra to find the y intercept. What doesthe y intercept represent?
3. Use algebra to find the x intercept. What doesthe x intercept represent?
4. Discussthe coordinatesof the vertex. Whatdoes thisrepresent?
5. Is thisa reasonable graphfor a missile launch? (Commentonlaunch height andlocation, max altitude and
landingsite)
F
1. Draw the missile launchof y=-5x2
+30x+2
2. Use algebra to find the y intercept. What doesthe y intercept represent?
3. Use algebra to find the x intercept. What doesthe x intercept represent?
4. Discussthe coordinatesof the vertex what does thisrepresent?
5. Use algebra to find the height abovethe groundwhen the missile has
travelled 3000kms

4. 6. Use algebra to decide after what distancesthe missile is 27 000kmabovetheground?
7. Are these answers realistic for a missile launch? (Commenton launchheight and location, max altitudeand
landingsite)
G
1. Draw the missile launchof y= -x2
+2x+3
2. Use algebra to find the y intercept. What doesthe y intercept represent?
3. Use algebra to find the x intercept. What doesthe x intercept represent?
4. Use the axis of symmetry tofind the coordinates of the vertex. Whatdoes
this represent?
5. Use algebra to find the height abovethe groundwhen the missile hastravelled 3000kms
6. Use algebra to decide after what distancesthe missile is 27 000kmabovetheground?
7. Are these answers realistic for a missile launch? (Commenton launchheight andlocation, max altitudeand
landingsite)
H
1. Draw the missile launchof y= -2x2
+3x
2. Use algebra to find the y intercept. What doesthe y intercept represent?
3. Use algebra to find the x intercept. What doesthe x intercept represent?
4. Use the axis of symmetry tofind the coordinates of the vertex. Whatdoes
this represent?
5. Are these answers realistic for a missile launch? (Commenton launchheight andlocation, max altitude and
landingsite)
6. If this missile was aimed at Japan, would it hit the mark?Why/why not?

5. I
1. Draw the missile launchof y= -5x2
+16x
2. Use algebra to find the y intercept. What doesthe y intercept represent?
3. Use algebra to find the x intercept. What doesthe x intercept represent?
4. Use the axis of symmetry tofind the coordinates of the vertex. Whatdoes
this represent?
5. Are these answers realistic for a missile launch? (Commenton launchheight andlocation, max altitudeand
landingsite)
6. If this missile was aimed at Guam, wouldit hit the mark?Why/why not?
J
1. Draw the missile launchof y= -0.15(x-4)2
+3
2. Use algebra to find the y intercept. What doesthe y intercept represent?
3. Use algebra to find the x intercept. What doesthe x intercept represent?
4. Use the axis of symmetry tofind the coordinates of the vertex. What
does thisrepresent?
5. Are these answers realistic for a missile launch? (Commenton launchheight andlocation, max altitudeand
landingsite)
6. If this missile was aimed at Japan, would it hit the mark?Why/why not?
Assumptionsandlimitations:
When calculating missile trajectories what assumptionsandlimitationshavebeen made?

6. Patterns observed:
For the equationy= ax2
+bx + c
Have younoticed any patternsregarding:
1. Whether the graphis concaveor convex?
2. The skinniness/fatnessof the graph?
3. The positionof the graph onhorizontal/ vertical axis
4. The axis of symmetry andvertex of the graph
“SEOUL— North Korea’spowerfulnucleartestthismonth may havebeen even strongerthan firstreported, equivalent
to roughly 17 timesthestrength ofthebomb thatdestroyed Hiroshima, according to a newanalysisby a U.S.
monitoring think tank.”(Washington Post2017)
1. A nuclear missile sent by Korealands ona deserted island. The weight of nuclear decay is represented by
W=1.9 x0.95t
tonnesperyear.
a) Algebraically find the initial weight of the nuclear content
b) Algebraically find the weight after: i) 22yrs ii) 35yrs iii) 100yrs
c) If the island is deemed safe when the level of nuclear waste reaches 0.0001 tonnes. Onwhatyear will the
island be safe to inhabit. (Show algebraically usinglogarithms)
d) Draw the graph andshow youranswers to a,bandc on the graph
e) According to the model will there ever be nonuclear waste onthe island?

7. 2. Thankfully the trees onthe island are beginning to grow back. There were 15 trees remaining at after the blastand
their rate of growth is 5% per year.
a) Write anequation torepresent the numberof trees on the island
b) Algebraically show how many trees there will be after:
i) 5 years ii) 50 years iii) when the islandcan be inhabitedagain
C) The islandis deemed environmentally friendly when there are 50 trees onit. Show algebraically on what year
this will occur (use logarithmsto solve).
d) Draw the graphand showyouranswers to a,band c on the graph
f) Lookingat the graph why mightn’tanexponential model be appropriatefor thisscenario?
Assumptionsandlimitations:
When calculating solutionswhatassumptionsandlimitationshavebeen made?

8. Conclusion:
See Folio Exemplar and feedback from previous folios.
Marking will be done according to the SACE rubric.
Bibliography:
ABC News (2017)WherecouldaNorthKoreanintercontinentalballisticmissilehit?Accessed14/09/17http://www.abc.net.au/news/2017-
07-04/where-could-a-north-korean-icbm-hit/8678296
WashingtonPost(2017)NorthKoreanuclear test may havebeen twice as strongasfirst thoughtAccessed 14/09/17
https://www.washingtonpost.com/world/north-korea-nuclear-test-maybe-have-been-twice-as-strong-as-first-
thought/2017/09/13/19b026d8-985b-11e7-a527-3573bd073e02_story.html?utm_term=.ea7454b610d2