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The maximum range of a gun on horizontal terrain is 16 km. If g = 10 m/s², then muzzle velocity of a shell must be

1. 160 ms⁻¹
2. 200√2 ms⁻¹
3. 400 ms⁻¹
4. 800 ms⁻¹

Correct answer: 400 ms⁻¹

Solution

The maximum range of a projectile is given by R = (v²/g), where v is the muzzle velocity. Rearranging, v = √(Rg). Substituting R = 16,000 m and g = 10 m/s², we get v = √(16,000 × 10) = 400 m/s.

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