Projectile Motion Calculator

About projectile motion

Projectile motion describes the motion of an object launched into the air under the influence of gravity. For most problems we neglect air resistance and assume constant gravitational acceleration g ≈ 9.81 m/s^2 downward. The initial velocity is decomposed into horizontal and vertical components: u_x = u cos θ and u_y = u sin θ. The horizontal motion is uniform (constant velocity) and the vertical motion is uniformly accelerated. Using these, we calculate time-of-flight, maximum height, and horizontal range. This calculator computes results given an initial speed and launch angle, optionally with an initial height. The time of flight with initial height y0 is found by solving a quadratic in t for vertical position y(t) = y0 + u_y t - 0.5 g t^2 = 0; the physically relevant root is the positive time when the projectile returns to ground level. Maximum height occurs at t = u_y / g and the range is u_x times time-of-flight. These formulas are sufficient for most NCERT and JEE style problems; for more advanced practice include air drag or non-level landing surfaces.

Use this tool to practice a variety of JEE-style numericals: change initial height to model higher launch points, vary the angle to find the optimal 45° for maximum range (on level ground), and compare calculated results with hand-worked steps to strengthen problem solving under time constraints.