Distance Calculation for a Steel Ball Rolling off a Table
How can we predict where a steel ball will land when it rolls off a table?
In a lab experiment, you need to predict where a steel ball will land when it rolls off a table that is 0.8 meters high. If the ball travels on the table with a constant velocity and travels 1.2 meters in 3.0 seconds, how far from the base of the table will the steel ball land?
Answer:
The steel ball will land 44.1 meters below the table.
To predict where the steel ball will land when it rolls off the table, you would need to calculate the distance the ball travels horizontally (x) as well as the distance the ball travels vertically (y). Since the ball travels on the table with a constant velocity, you can use the kinematic equation:
y = vi_y*t + (1/2)at^2
where y is the final vertical distance, vi_y is the initial vertical velocity (0, since the ball is rolling off the table), t is the time (3 seconds), and a is the acceleration due to gravity (-9.8 m/s²).
By substituting the values into the equation:
y = 0*3 + (1/2)(-9.8)*3² = -44.1 meters
Therefore, the steel ball will land 44.1 meters below the table.