(a) A ball is thrown in an upward direction. If the variable xx represents the velocity of the ball when it strikes the ground. Classify variable xx as discrete or continuous. Justify your answer with a proper explanation.
Answer:
Introduction
The problem asks us to classify the variable xx, which represents the velocity of the ball when it strikes the ground, as either discrete or continuous. To do this, we need to understand the nature of the variable and how it can take values.
Work/Calculations
Understanding Discrete and Continuous Variables
Discrete Variable: A variable is considered discrete if it can take only specific, separate values. For example, the number of students in a classroom can only be a whole number; it cannot be a fraction or a decimal.
Continuous Variable: A variable is considered continuous if it can take any value within a given range. For example, the height of a person can be any value within a certain range, including fractions and decimals.
Classifying the Variable xx
The velocity xx of the ball when it strikes the ground can take any value within a given range, depending on various factors like the initial velocity, angle of projection, air resistance, and gravitational force. It is not restricted to specific, separate values. Therefore, xx can be any real number within a certain range.
Let’s classify the variable xx:
“Variable “x=”Continuous”\text{Variable \( x \)} = \text{Continuous}
Conclusion
The variable xx, which represents the velocity of the ball when it strikes the ground, is a continuous variable. This is because it can take any value within a given range and is not restricted to specific, separate values.