A gun if mounted on a plateau 960 m away from its edge as shown. Height of plateau is 960 m. The gun can fire shells with a velocity of 100 m/s at any angle of the following choices, what is the maximum distance (OP) x from the edge of plateau where the shell of gun can reach?

Question

G1 Physics · Accepted Answer

The shell must first clear the 960 m long plateau. For the maximum reach beyond the edge, the lower limiting launch angle is the one whose same-level range is exactly 960 m: u²sin2θ/g = 960. With u = 100 m/s and g = 10 m/s², sin2θ = 0.96, giving the lower angle with sinθ = 0.6 and cosθ = 0.8. Then uₓ = 80 m/s and uᵧ = 60 m/s. To reach the lower ground 960 m below: -960 = 60t - 5t², so t = 6 + 2√57 ≈ 21.10 s. Horizontal distance from the gun is ≈ 1688 m, hence from the edge x ≈ 728 m, closest to…