1 2 1 htv gt + + /

MPM2D
Applications of Quadratics
Date ______________
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gt + v0 t + h0 can be used to model the height of a projectile,
2
where g is acceleration due to gravity, which is 9.8 m / s 2 on Earth, v0 is the initial vertical
velocity, in metres per second, and h0 is the initial height, in metres.
G roup 1 : The formula h = −
a) Create a model for the height of a toy rocket
launched upward at 60 m / s from the top of a
3-m platform.
b) How long would the rocket take to fall to Earth,
rounded to the nearest hundredth of a
second?
c) What is the maximum height of the rocket,
rounded to the nearest metre?
d) Over what time interval is the height of the toy
rocket greater than 150 m? Round to the
nearest hundredth of a second.
G roup 2 . : A rectangular park measures 100 m by 60 m. A path of constant width is to be paved
around the perimeter. The mayor wants to be sure that the path does not reduce the area of
grass by more than 10%. What is the maximum allowable width of the path, rounded to the
nearest tenth of a metre?
G roup 3 . : The product of two consecutive even numbers is 5624. What are the numbers?
G roup 4 . : One leg of a right triangle is 1 cm longer than the other leg. The length of the
hypotenuse is 9 cm greater than that of the shorter leg. Find the lengths of the three sides.
G roup 5 . : A small canoe-rental business charges $12/canoe and averages 36
rentals a day. The owner knows that for every $0.50 increase in rental prices,
there will be a loss of two rentals a day. Also, for every $0.50 decrease, there will
be a gain of two customers. Use this information to maximize the revenue. How
much should the owner charge?
G roup 6 . : Merlin is at the casino. He has a meter stick and breaks it randomly
into two pieces. He then uses these pieces to form the legs of a right triangle
and computes the area of the triangle. If the area is more than 0.15 m2, you
win $50. If the area is less, you pay him $5. Would you play this game? (If the
area is negative, he sizzles you to death with a lightning bolt).
Group 7.: Harold wants to build five rectangular identical pig pens, side by side, on his farm
using 30m of fencing. Determine the dimensions of the enclosure that would give his pigs the
largest possible area. Calculate this area.
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