Problem 89 - College Algebra

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I threw a baseball vertically upward and its path was a parabola.

Step-by-Step Solution

Answer

The statement does not make sense. Though a projectile usually follows a parabolic path, a baseball thrown directly upward will not as it lacks the horizontal motion necessary to create a curved trajectory.

Step 1: Analyze the Statement

In the statement, a baseball is thrown vertically upwards. It is claimed that this baseball follows a parabolic path.

Step 2: Examine Properties of a Parabola

A parabola is a curve where any point is at an equal distance from a fixed point (the focus), and a fixed straight line (the directrix). In the real world context, the path of a projectile is typically parabolic due to the force of gravity acting downwards on the object.

Step 3: Compare Statement to Properties of a Parabola

In the given scenario, a baseball is thrown vertically upwards. This means the baseball has no horizontal motion, it only moves upwards and then downwards. Since the path lacks horizontal motion, it doesn't create a curve shape but a straight line. Thus, we can conclude that the path of the baseball is not a parabola.