Projectile Range

Per NCERT Class 11, Chapter 4 (Motion in a Plane), the horizontal range of a projectile on level ground is R = (u² sin2θ) / g, which combines the launch speed, the launch angle, and gravity. With u = 40 m/s, θ = 45°, sin2θ = sin90° = 1, so R = (40² × 1) / 10 = 1600/10 = 160 m. The option 80 m results from forgetting to square the velocity or halving the result. The option 320 m doubles the range by mistakenly using 2u² in the numerator. The option 120 m has no consistent derivation and underestimates the range. Plausibility check: 45° is the angle of maximum range for a given speed, and the time of flight is 2u sinθ/g = 2(40)(0.707)/10 ≈ 5.66 s; multiplying by the horizontal velocity u cosθ ≈ 28.3 m/s gives about 160 m, confirming the standard range formula result.