i.
To state: The heights that the basketball player and the kangaroo jumped if "Hang time" is the time you are suspended in the air during a jump.
The heights that the basketball player and the kangaroo jumped are
Given information:
The function is
Hang time of the basketball player is
Calculation:
Write the given equation:
Divide both sides of the equation by 0.5,
Square both sides of the equation,
Now substitute
Now substitute
Therefore, the jump height of basketball player and that of kangaroo are
ii.
To state: The corresponding heights of each jump after doubling the hang times of the basketball player and the kangaroo.
The new heights that the basketball player and the kangaroo jumped are
Given information:
Double the hang times of the basketball player and the kangaroo.
New hang time of the basketball player is:
New hang time of the kangaroo is:
Explanation:
Now substitute
Now substitute
Therefore, the new jump height of basketball player and that of kangaroo are
iii.
To state: If the hang time doubles, does the height of the jump double? Explain.
Doubling the hang time results in 4 times of the jump height.
Given information:
The statement says, “Does doubling the hang time double the height of the jump?”
Explanation:
Original heights of the jump are:
Basketball player:
Kangaroo:
New heights of the jump after doubling the hang time are:
Basketball player:
Kangaroo:
Now check if the height doubles after doubling the hang time:
For the basketball player:
For the kangaroo:
It is clear that doubling the hang time results in 4 times of the jump height.
The relation between the hang time and the jump height is shown below:
The height of the jump is not directly proportional to the hang time. It is proportional to the square of the hang time.
Chapter 3 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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