Final answer:
To determine the acceleration due to gravity, a metal sphere should be dropped vertically, as the experiment aims to show that gravitational acceleration is constant, regardless of an object's initial velocity. Data on the time to impact for each ball in the experiment is needed, and the final velocity can be calculated using the equation related to height, gravitational acceleration, and final velocity.
Step-by-step explanation:
To determine the acceleration due to gravity, a small metal sphere should be dropped vertically downward in the coordinate system. Dropping the sphere vertically ensures that it is only subject to gravity and not any other forces such as air resistance or thrust that could affect its horizontal motion. Therefore, the correct answer is a) Vertically.
When considering the ball's horizontal velocity in projectile motion, the graph would be a horizontal line assuming no air resistance, indicating a constant horizontal velocity. However, the vertical acceleration graph versus time would be a horizontal line at the value of gravitational acceleration (approximately 9.8 m/s2 on Earth), showing that the acceleration is constant over time, irrespective of the object's velocity.
For the experiment, the student would need to collect data on the time it takes for each ball to hit the ground to demonstrate that acceleration due to gravity is independent of the ball's initial velocity or horizontal motion.
To calculate the velocity of an object as it hits the ground when you know the height from which it was dropped, you can use the equation v = sqrt(2gh), where v is the final velocity, g is the acceleration due to gravity, and h is the height.