Projectile Motion

The question behind the experiment

A projectile follows a curved path, but its horizontal and vertical motion can be analyzed separately. This course uses launch and landing measurements to connect that decomposition to evidence. Decide whether the launcher is horizontal or angled and whether launch and landing occur at the same height. Those choices determine the appropriate flight-time and range relationships. A remembered range formula is useful only when its assumptions match the apparatus you have selected for the investigation.

Plan a useful comparison

Begin with horizontal launches from a fixed height. Change the launch-speed setting while holding the height and direction constant. Predict which measured quantity changes: flight time, horizontal distance, or both. Retain the launcher setting and height beside every landing record. If you change height at the same time as speed, a longer range no longer isolates the effect of faster horizontal motion. Repeat the comparison using a different height as a separate investigation.

Connect the observation to the model

Use vertical motion to determine the time available for horizontal travel. In the ideal horizontal-launch model, the initial vertical velocity is zero and gravity produces the downward acceleration. Horizontal distance then follows from horizontal speed multiplied by flight time. Compare a graph of range against speed with a graph of squared flight time against height. These graphs reveal different parts of the model, so label both axes with the quantities and units actually measured in the trial.

Interpret the result carefully

For angled launches, resolve the initial velocity into horizontal and vertical components. At the top of the path, vertical velocity can be zero while downward acceleration persists. The projectile has not lost its horizontal motion. Compare complementary launch angles only when the launch and landing heights match and the ideal assumptions apply. An elevated launcher or a different landing surface changes the symmetry. Explain those conditions before predicting that two angles should produce equal ranges.

Build an explanation from your evidence

The apparatus connects prediction to practical measurement choices, including landing marks and photogate timing. A collection of landing positions supports a repeatability estimate rather than a single perfectly placed mark. A photogate measures speed through a finite interval, so its geometry belongs in the speed calculation. Distinguish the ideal gravity-only trajectory from modeled real-lab variation. The purpose is to evaluate a prediction against recorded evidence, not to infer a universal launcher calibration from a drawing of the path.

A reference case from this course

For the Ideal horizontal-launch case at height 1.00 m, the course gives a flight time of 0.4517539515 s for each of its launch-speed settings. The equal times apply to that fixed height and zero initial vertical velocity. They do not imply that every angled launch has the same time in the air.

Keep the investigation reproducible

Before changing the setup, write a prediction that names the measured quantity and the expected direction of change. Retain the original trial as a reference. Record the apparatus conditions, units, and whether you used Ideal or Real lab mode. If the selected activity includes seeded variation, keep the seed and run identity with the result so another comparison does not silently mix different conditions.

Separate the observation from its explanation. A reading or a counted object belongs in the evidence; the relationship you use to interpret it belongs in the reasoning. When a result differs from the reference case, check the settings and measurement procedure before deciding that the model relationship has failed. Describe a specific source of uncertainty and where it enters your calculation. Finish with a claim supported by the recorded comparison, and identify an additional trial that could distinguish your explanation from an alternative.

Continue the comparison

Use Motion Graphs & Reference Frames to interpret signed velocity traces, then explore the energy account in Energy Conservation. Compare motion measurements and energy measurements as complementary descriptions of a matched setup.