Final answer:
To measure an object's maximum height in ballistic motion, initial velocity, gravitational acceleration, and initial position are needed. Air resistance can affect the motion, so it must be considered, and a time of flight vs. height graph is predicted to be parabolic.
Step-by-step explanation:
To calculate the maximum height an object reaches, the following variables are required: initial velocity (Ωo), gravitational acceleration (g), and the initial vertical position (yo). The maximum height is achieved when the vertical velocity component (vy) becomes zero; at this point, the object stops ascending and begins to descend.
The equation used to find the maximum height (y) is v² = v²o - 2g(y - yo), where v is the final velocity which is 0 at the apex of the trajectory. To conduct a two-dimensional ballistic motion experiment, one must measure the time of flight and the maximum height reached by the object. As ballistic motion is symmetrical, measuring these factors at half the time of flight would suffice since the ascent and descent times are equal.
If there is no horizontal component to the object's velocity, the object would simply travel straight up and straight down, not affect the measurement of the maximum height directly but changing the dynamics of the trajectory.
Air resistance, if significant, would reduce the maximum height achieved and the object's time of flight, so it must be considered when designing experiments and interpreting results. A graph of travel time versus maximum height is predicted to be parabolic due to the squared relationship between velocity and displacement in the equation of motion.