Final answer:
The dependent variable in the statement is the 'speed of the baseball' since it is the effect being measured in response to the independent variable, which is 'how hard Sam throws the ball'. To design an experiment to show acceleration's independence from velocity, the student would need to record the time it takes for different balls to launch under varied conditions to reach the ground.
Step-by-step explanation:
The statement "The harder Sam throws the baseball, the faster the baseball travels" helps us to identify the dependent variable and the independent variable. The independent variable is the one that is controlled or manipulated, in this case, 'how hard Sam throws the ball'. Therefore, as 'how hard Sam throws the ball' is the cause, it's the independent variable. The dependent variable, on the other hand, is the one that is measured and is expected to change when the independent variable is manipulated. So, the 'speed of the baseball' is the dependent variable, as it is the effect that changes in response to how hard Sam throws the ball.
When designing an experiment, it's critical to clearly define these variables. For example, if a student wanted to show that acceleration is independent of an object's velocity, they would need to make observations that can confirm or refute this hypothesis. To do this, they would need to compare the time it takes for each ball—launched under different conditions but from the same height—to hit the ground. Since acceleration due to gravity should be constant, the times recorded should be the same, demonstrating that acceleration is constant irrespective of the object's velocity. Thus, this would suggest the independence of acceleration from the initial velocity of each ball.