Projectile Motion Experiment Calculator

A projectile motion experiment tests the independent horizontal and vertical parts of motion. Once an object leaves a launcher, the ideal model gives it constant horizontal velocity and constant downward acceleration. The launch speed is resolved into vx = v cos θ and vy = v sin θ. Measuring those components indirectly through distance and time lets students compare observed motion with the kinematic equations and examine where a physical apparatus departs from the simplified theory. This calculator is designed for a launch and landing at the same elevation. Under that condition, the time to rise equals the time to fall, so total flight time is 2vy / g. Multiplying that time by vx gives horizontal range. Maximum height above the launch point is vy² / 2g. These formulas assume the launch begins at time zero, the object can be treated as a point mass, gravity is uniform, and aerodynamic forces are negligible. The displayed velocity components are also useful when preparing data tables or checking photogate measurements. A careful experiment starts by measuring launch speed rather than relying only on a launcher setting. Two photogates a known distance apart can estimate speed, while video tracking can derive position and velocity over time. Measure launch angle from the horizontal and verify that the landing surface is level with the release point. If the landing level differs, use a general projectile model with initial height because the symmetric flight-time equation on this page will no longer apply. Experimental uncertainty should be recorded for speed, angle, distance, and time. Angle error often has a strong effect because both sine and cosine depend on it. Repeat launches and calculate a mean range rather than judging the theory from one trial. Compare predicted and measured values with percent difference, but consider measurement resolution and systematic effects before concluding that a discrepancy is significant. Launcher friction, spin, air drag, an uneven floor, delayed timing, and uncertainty in the exact release point can all shift the result consistently. The standard gravity value is prefilled, and it can be adjusted to a locally measured value or changed for a simulated experiment on another world. Use meters, seconds, and degrees in every field. The ideal level-ground range is greatest at 45 degrees, while complementary angles such as 30 and 60 degrees produce the same range in the model but different heights and flight times. Testing those relationships makes a useful extension to a basic lab. This calculator provides a theoretical baseline, not fabricated experimental data. Preserve your actual observations, apparatus settings, uncertainty estimates, and environmental conditions separately. It is appropriate for classroom demonstrations, lab preparation, hypothesis checks, and analysis of low-speed projectiles. Use soft projectiles, eye protection, a secure backstop, and an exclusion area appropriate to the apparatus; never launch an object where an unexpected path could injure a person or damage property.