Chapter 7 Practice Test With Answers - Montville Township Public Schools Page 8
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92
= t(40) sin 60 −
(32)t
+ 5
18.
CAMPING In many U.S. parks, campers must
secure food and provisions from bears and other
Practice Test - Chapter 7
animals. One method is to secure food using a bear
Graph the equation for the vertical position and the
bag, which is done by tossing a bag tied to a rope
line y = 30. The curve will intersect the line in two
over a tall tree branch and securing the rope to the
places. The second intersection represents the bag
tree. Suppose a tree branch is 30 feet above the
as it is moving down toward the branch. Use 5:
ground, a person 20 feet from the branch throws the
intersect function on the CALC menu to find the
bag from 5 feet above the ground.
second point of intersection with y = 30. The value is
a. Will a bag thrown at a speed of 40 feet per
about 1.89 seconds.
second at an angle of 60º go over the branch?
b. Will a bag thrown at a speed of 45 feet per
second at an angle of 75º go over the branch?
Determine the horizontal position of the bag at 1.89
seconds.
SOLUTION:
= tv
cos θ
x
a . To determine whether the bag will go over the
0
branch, you need the horizontal distance that the bag
= 1.89(45) cos 75
has traveled when the height of the bag is 30 feet.
≈ 22.01
First, write a parametric equation for the vertical
position of the bag.
The bag will travel a distance of about 22.01 feet
before the height reaches 30 feet a second time.
2
y
= tv
sin θ −
gt
+ h
0
0
Since the bag is being thrown from a distance of 20
feet from the tree, the bag will make it over the
2
= t(40) sin 60 −
(32)t
+ 5
branch.
Use a graphing calculator to graph the conic
Graph the equation for the vertical position and the
given by each equation.
line y = 30. The curve does not intersect the line.
2
2
19.
– 6xy + y
– 4y – 8x = 0
x
Therefore, the height of the bag never reaches 30
feet and the bag will not make it over the branch.
SOLUTION:
Graph the equation by solving for y.
2
2
= 0
– 6xy + y
– 4y – 8x
x
2
2
= 0
y
+ (–6x − 4)y + x
− 8x
b. To determine whether the bag will go over the
branch, you need the horizontal distance that the bag
has traveled when the height of the bag is 30 feet.
First, write a parametric equation for the vertical
position of the bag.
2
y
= tv
sin θ −
gt
+ h
0
0
2
= t(40) sin 60 −
(32)t
+ 5
Graph the equation for the vertical position and the
line y = 30. The curve will intersect the line in two
[–10, 10] scl: 1 by [–10, 10] scl: 1
places. The second intersection represents the bag
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Page 8
as it is moving down toward the branch. Use 5:
2
2
20.
x
+ 4y
– 2xy + 3y – 6x + 5 = 0
intersect function on the CALC menu to find the
second point of intersection with y = 30. The value is
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