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Concept explainers
b.
To calculate the height from which the ball was hit.
b.
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Answer to Problem 63PPS
The height from which the ball was hit is the ground level, or,
Explanation of Solution
Given information :
The function provided is
Formula used :
To compute the height from which the ball was hit, find the y-intercept of the given equation.
y-intercept is computed by substituting the value of t in the equation by 0
Calculation :
Simplifying
Hence the point of y-intercept is
Thus the ball was hit from the ground level at
c.
To calculate maximum height reached by the ball.
c.
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Answer to Problem 63PPS
The maximum height reached by the ball is
Explanation of Solution
Given information :
The function provided is
Formula used :
The maximum height attained by the ball can be calculated by finding the vertex of the equation.
Formula to compute equation of the axis of symmetry
Axis of symmetry for the given function is
Put this value of x in the main function to get h this will be maximum height.
Calculation :
Axis of symmetry for the given function is
Formula for axis of symmetry.
Putting the values of ‘a’ and ‘b’ .
Simplifying this
Vertex can be found out by putting the value of x computed in the axis of symmetry in the original function. This will give a value of y . These two coordinates of x and y would be the point where the vertex is.
Putting the value of
Simplifying the expression.
Thus the maximum height reached is
d.
To calculate the time taken by the ball to hit the ground.
d.
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Answer to Problem 63PPS
The time taken by the ball to hit the ground is
Explanation of Solution
Given information :
The function provided is
Formula used :
To calculate the total time taken, use the formula to find roots of a
Here,
Calculation :
Putting the values in the formula.
Simplifying
Removing square root.
One of the roots simplifications.
This is the first root.
Second root’s simplification.
Dividing the fraction.
Thus, the ball hits the ground at
e.
To mention a reasonable domain and range for the given equation.
e.
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Answer to Problem 63PPS
A reasonable domain for this function would be
Explanation of Solution
Given information :
The function provided is
Since the given function is a quadratic one, the graph is that of a parabola. In case of a parabola, the domain is all values with t can take. This is case, it is evident that the ball would not have a negative time and neither would the value of h be negative. Thus, the domain is
Had this curve not represented any ball moving trajectory, the domain would have been all real numbers while the range would have been
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Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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