A shell of muzzle speed 45 m s⁻¹ is fired from the tail gun of an aeroplane moving horizontally at 215 m s⁻¹. The gun can be directed at any angle with the vertical in the plane of motion. The shell is fired when the plane is above ground point A, and the plane is above point B when the shell hits the ground. Which landing locations are possible?
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Question

A shell of muzzle speed 45 m s⁻¹ is fired from the tail gun of an aeroplane moving horizontally at 215 m s⁻¹. The gun can be directed at any angle with the vertical in the plane of motion. The shell is fired when the plane is above ground point A, and the plane is above point B when the shell hits the ground. Which landing locations are possible?

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G1 Physics · Accepted Answer

The shell retains the aircraft's large forward ground velocity plus/minus at most 45 m s⁻¹ horizontally. It cannot land behind A. By suitable gun direction it can have the same horizontal speed as the plane and land at B, or greater effective forward displacement and land ahead of B. Source key: B,D.