Horizontal Range Projectile Motion — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Horizontal Range (Projectile Motion) Applicable only for projectile motion over a flat surface where the launch height equals the landing height, ignoring air resistance. Determine time of flight t by setting vertical displacement to zero: 0 = (v0 sin theta)t - 0.5 g t 2. Solve for t (non-zero solution): t = 2 v0 sin theta / g. Substitute t into the horizontal motion equation: R = (v0 cos theta) t. Combine terms: R = v0 cos theta (2 v0 sin theta / g) = v0 2 (2 sin theta cos theta) / g. Apply double angle identity sin(2 theta) = 2 sin theta cos theta. y final = y initial (Zero net vertical displacement) No air resistance Constant gravitational acceleration 0 <= theta <= 90 degrees Applying this formula when the projectile lands on a higher or lower surface (e.g., cliff problems). Assuming the angle for maximum range is always 45 degrees (only true if launch/land heights are equal). Confusing the launch angle with the angle of impact.