A gun is 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 minimum distance (OP) x from the edge of plateau where the shell of gun can reach?

Question

G1 Physics · Accepted Answer

To reach the lower ground without striking the plateau, the same-level range must be at least 960 m. The minimum distance beyond the edge occurs for the higher limiting angle with same-level range exactly 960 m. Since u²/g = 1000 m, sin2θ = 0.96; for the higher angle, sinθ = 0.8 and cosθ = 0.6. Thus uₓ = 60 m/s and uᵧ = 80 m/s. Solving -960 = 80t - 5t² gives t = 24 s. The horizontal distance from the gun is 60×24 = 1440 m, so distance beyond the edge = 1440 - 960 = 480 m. Hence option A.