Suppose that in one stunt, two Cirque du Soleil performers
seesaws. The first performer
are launched toward each other from two
is launched, and 1 s later the second performer
both perform a flip and give each other a high five in the air. Each performer
seesaw versus time for each performer
during the stunt is approximated
height of the first performer versus time is h
time is h
a.
= -5{t
= -5(t
- 2)2 + 5. When are the performers
lightly offset
is launched in the opposi
direction. They
is in the air for 2 s. The h ight above the
by a parabola as shown. The
quation for the
- 1)2 + 5. The equation for the height of the second
erformer versus
at the same height so they can give each other a hi
five?
Write a system that will model this situation:
[
-::.-
L
fr)
=- -
5( -f _/)2. ..L 5
'?
(+ -l) '2-T 5
b.
Solve the system using substitution and factoring/quadratic formula:
c.
List the ordered pairs:
d.
Solution Sentence:
-
(1.5", 3115)
'5 (+ -()l.t5:: -5(t-2.)2+5
- S l t -I) 2.
(t -I )2.::
~ -
5 (t -2)'l.
f _{)"2
1+ +akes J, 5" Sec.~s ~'f tht m ~ r-.eQch a
~j d'at o~ 3,1 S WIrt(XL -1hUj cu.rt S1oc elA.('t,
O~t,('
o: h\~ ~I/t
A car manufacturer
.
does performance
tests on its cars. During one test, a car starts from rest and acc erates at a
constant rate for 20 s. Another car starts from rest 3 s later and accelerates at a faster constant rate.
e equation that
models the distance the first car travels is d :: 1.16t2 , and the equation that models the distance the s cond car travels is
d
= 1.74(t
- 3)2 , where t is the time, in seconds, after the first car starts the test, and d is the distance,
long will it take for the two cars to have traveled the same distance?
.
a.
-t'l.
d ; (0 .
d =-1.1 4- (~-3»
Write a system that will model this situation;
b.
Solve the system using substitution and factoring/quadratic formula:
c.
List the ordered pairs:
(I. tos \ \.p ) 3 .llo4 a)
d.
.
Solution
(/10
Sentence:
1...
/.1
db
\.~5\~.Q.('
2-
=
2
(ot
"l.::.
I fllf-t'-IO.<-f4t+{Z),fIp
o = #5 t2..-10. t.ti+I5,b"
t z: IO,tt :± [lo.y...l--t.t( !~)(rf,C,{,
.3~8"'h3\0.0334')
2-(·58)
Iht 1wa (U(S iYaLXJ 1ttS4:VU dl&+l.tnu..
~
How
l. i 'I [f ..3)
LI(at~.:1.1tf{ta.-/o +4)
I. I ~
l
n metres.
t: =- 10. '+1.../ ± 172.& f;;zl/
and I~· atitt( ..sfC.
i. I V;
t::IO·4
j:~.l52¥:;}
./~
A Canadian cargo plane drops a crate of emergency supplies to aid-workers on the ground. The crate
before a parachute opens to bring the crate gently to the ground. The crate's height, h, in metres, ab
seconds after leaving the aircraft is given by the following two equations. h
= -4.9t2 + 700
represents t e height of the
crate during free fall. h = -St + 650 represents the height of the crate with the parachute open. a) Ho
crate leaves the aircraft does the parachute open? Express your answer to the nearest hundredth
{h'h"=-- 4
of
height above the ground is the crate when the parachute opens? Express your answer to the nearest·
IQ-(L+700
5i: -f-ioSO
a.
. a system th at will mo de1thiss Situation:
si
.
Wnte
b.
Solve the system using substitution and factoring/quadratic formula:
-.
rops freely at first
e the ground t
long after the
second. b) What
etre.
During a basketball game, Ben completes an impressive "alley-oop."
From one side of the hoop, his te mmate Luke lobs
a perfect pass toward the basket. Directly across from Luke, Ben jumps up, catches the ball and tips it
2
The path of the ball thrown by Luke can be modelled by the equation d
-
to the basket.
2d + 3h = 9, where d is the h rizontal distance
of the ball from the centre of the hoop, in metres, and h is the height of the ball above the floor, in m
ers. The path of
10d + h = 0, where d is his horizontal distance from
he centre of the
Ben's jump can be modelled by the equation
5d2 -
hoop, in metres, and h is the height of his hands above the floor, in metres. a) Solve the system of equ tions
h~ -d 2.+ld q
algebraically. Give your solution to the nearest hundredth.
a.
w'
rite a system
th
at
will
d 1this si
.
mo e
s Situation:
-tJn::: q
Lf Sdd 2._2
2..._1 Od +h::: 0
b.
Solve the system using substitution and factoring/ quadratic formula:
c.
List the ordered pairs:
d.
d
-= -d ~l.d +c,
.3
-I ":)d'+ od e -d Z+2.d q
o /4d 1._2~-eL+q
Solution Sentence:
\h t
.3
h:; _ Sd !.+\
bcdl o..nd Ben mt~+ , 3~q
S'-(Ctl ~
~+~ t~f3
I
i'11(
'f.
P.."
d-
o..'os\tt. 4lt.. {' 100 r,
The 20l5-m-tall
Mount Asgard in Auyuittuq
National Park, Baffin Island, Nunavut, was used in the op
ing scene for the
James Bond movie The Spy Who Loved Me. A stuntman skis off the edge of the mountain, free-falls fo several seconds,
and then opens a parachute. The height, h, in meters, of the stuntman above the ground t seconds a
edge of the mountain
is given by two functions.
opens the parachute. h(t)
h(t)
= -4.9t2 + 2015
represents the height of the stunt
r leaving the
an before he
= -10.5t + 980 represents the height of the stuntman after he opens the par chute. a} For how
many seconds does the stuntman free-fall before he opens his parachute? b) What height above the
1..'2-
stuntman when he opened the parachute?
) h(±}~-4t
+1016
[ h Lt): ..
lO.;i': +ct~
a.
Write a system that will model this situation:
b.
Solve the system using substitution and factoring/ quadratic formula:
c.
List the ordered pairs:
©http://gabrielmathnorth.weebly
(I S ,~lw}~
round was the
)
~ll5 Ilqq~ ')
.com/uploads/l/2/6/9/l2696930/pre-calculus_ll_-
_chapter _ 8_ w bsite.pdf
The revenue for a production
production
, where t is the ticket price in dolla s. The cost for the
is y = 600 - SOt. Determine the ticket price that will allow the production
even when revenue = cost.)
a.
= - 5Ot2 + 300t
by a theatre group is y
Write a system that will model this situation:
r
H ::.-SDt
4-
8 == (DCO
-6'D
to break even. (
company breaks
:t30ot
...t..
L
b. Solve the system using substitution and factoring/ quadratic formula:
c.
3") LJ50)
List the ordered pairs: (
(4 )400)
d. Solution Sentence:
1hz -H-u..().:+,~Bro P
w II
t fb
b'l'-i-etL
e..uer I CL+aT)(lJi-pnl.l.. of is
a.PS'O ~ 1) clU.:tiVl·~~f;4 fbr o: Uor Ob
A daredevil jumps off the
r
Q
$'+00.
eN Tower
and falls freely for several seconds before releasing his parachute His height, h, in
meters, t seconds after jumping can be modelled by: h -4.9t2 + t + 360 before he released his parach te; and
=
h
= -4t
+142 after he released his parachute. How long after jumping did the daredevil release his par chute?
a.
Write a system that will model this situation:
r h::-4 .Glt "2-+-t ~
L
h:::.
~(t) 0
-L.%-t + IY "
b. Solve the system using substitution and factoring/quadratic formula:
c.
List the ordered pairs:
(-
<0. l 1q ) llo (p, 11
-4,Qt
t-=-
(p
'Z..
t ~-5:-
4~q7,'?'=-S.± b5.Sse
- ~Li
-q~i'
6~
-.. 2. se <..cnt.i.o.
i ~- /1 q ) 1, / 9qa
A punter kicks a football. Its height, h, in meters, t seconds after the kick is given by the equation
h = -4.9t2 + 18.24t + 0.8. The height of an approaching blocker's hands is modeled by the equation h
a.
f
h =- -
L\
,l1 t '2. + <6-,2.'t 1.
'e h~-'·tf~t
Solve the system using substitution and factoring/quadratic formula:
c.
List the ordered pairs:
d. Solution Sentence:
.
!)
Co.,;)
("3 ~"3)
- \ , '2.-\ \0 q )
L \%'4)
3/1Q,)
t
O. t
+4.~
b.
blocJu,.-
-1.43t + 4.26,
Can the blocker knock down the punt? If so, at what point will it happen?
Write a system that will model this situation:
~t.
5~ +2..\2':::.0
-'1,g
l-k Y'f-\eQs~s his ~c.ha:tt
using the same time.
.
-s± j5~Y.(-YfqXll6')
( 1 . 2 ) " 3. L ')
d. Solution Sentence:
,
-t 1'"3(00 = -'+t+lt.frl
-t.f,qt
- Y-,'lt2.+f8.
-4 .qt' -t-Iq.£o1t - •tflo =0
t '::
-~I
'0+ ~,q(fl Me
he' y.j'-
±J3IQ,fiiZ9
-IGilt
lV)oc.J(~-thl p.1l~
O-b1e,r ,g see and
Z4-t-r .~::; - '/t-~-t+"I.I"
t=
The height, h, of a baseball, in meters, at time t seconds after it is tossed out of a window is modelled y
h = - st2 + 20t + 15. A boy shoots at the baseball with a paintball gun. The trajectory of the paintball is iven by the
equation h = 3t + 3. Will the paintball hit the baseball? If so, when? At what height will the baseball b
a.
Write a system that will model this situation:
f h-:;.
- 5 -t £+1.0++ \5
?
"L h~3t+3
b.
Solve the system using substitution and factoring/quadratic formula:
c.
List the ordered pairs:
d.
Solution Sentence:
\+
IN it \
-5t~+llt
tZ--\lt-
~
a.
b.
.
The cost for the production
lL =-0
0
(t- - ~O X t + .3)
+:.~
of 11.
o: htts~
The revenue for a company producing electronic components
dollars of each component.
\'2-=- D
StL-llt
-hA\c..t . Lf se <.b')ds for-thL pa Ivrtba.U
to h\+-thL
production
-5t2+1..ot f?=3++3
t=..-3
6
"?
is given by y
=-
20x2
-
SOx + 200, wher
x is the price in
is given by y = 60x -10 .-Determine the price t at will allow the
to break even.
.
..
.
.
Wnte a system that will model this situation:
~~~-'2..Q>('2...-~x +l,OQ
2J::: <nDf..- t 0
.
Solve the system using substitution and factoring/quadratic formula:
-LOX.
4
X:t l..UJ.:: Wc»)(-,
.:-
- 2..ox 2._ \
I
~Ox.t.+\ \ 0
c.
List the ordered pairs:
d.
Solution Sentence:
A pv1~
( - -, )
-y. '30
(I.?)
30)
o-r 'tLSO
bY-~ t e-
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