One-dimensional motion describes the changes in the position of an object over time in terms of its displacement, velocity, and acceleration in one direction. The motion in that direction is independent of the displacement, velocity, and acceleration associated with any of the perpendicular directions. For example, the acceleration due to gravity near the surface of the earth has a value of 9.8 m/s², downward. This affects the vertical motion of an object but has no effect on the motion of the object in either of the horizontal directions. Thus, one-dimensional motion forms the foundation of our understanding of general motion in three dimensions.

Address one of three slightly different versions of the case of a ball falling to the base of a 50.0 m tall building.

• Neglect air resistance.
• The magnitude of the acceleration is 9.80 m/s².
• The eventual position of the ball is at the base of the building, 50.0 m below this initial position.
• Upward is defined as positive. Displacements, velocities, and accelerations directed upwards are positive. Conversely, if directed downwards, these same quantities are negative. Thus, the base of the building is located at -50.0 m, and acceleration is -9.80 m/s².

Answer the following questions. Support your answer with any necessary calculations.

• How long does the ball take to reach the base of the building?
• What is the final velocity of the ball just before striking the ground?
• Answer the additional questions for your Case as specified in the table below.

Freefall Case 1: Near the edge of the building the ball is thrown upward with an initial velocity of 14.7 m/s, at time t = 0.00 s.

Additional question: If downward were to have been chosen as the positive direction, how would this affect the values of displacement, velocity, and acceleration given in the description of the case study? Comment on the dependence of physical results, if any, on the choice of the positive direction chosen by observers.

Freefall Case 2: Near the edge of the building the ball is thrown downward with an initial velocity of -10.0 m/s, at time t = 0.00 s.

Additional question: How do the results of this case study change if the time when the ball is released is labeled 3.00 s, rather than 0.00 s? Comment on the dependence of physical results on the choice of labels, in this case, the initial time, chosen by observers. After the results of case 1 have been posted by at least one other student, compare your results for the final velocity of the ball and time to for the ball to fall to the results of case 1.

Freefall Case 3: Near the edge of the building the ball falls from rest to the base of the building. The words, "from rest" mean that the initial velocity 0.00 m/s.

Additional question: Comment on the similarity or differences in the final velocity (just before striking the ground) between this case study and either of the previous two case studies.