دراسة حركة قذيفة في مجال الثقالة المنتظم 2: 1/3
يمثل الشكل جانبه تبيانة مسار حركة قذيفة في مجال الثقالة المنتظم
![](data:image/png;base64,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)
نعتبر لحظة انطلاق القذيفة بسرعة تكون زاوية α مع المحور الأفقي, من النقطة O أصل المعلم (O,→i,→j)، أصلا للتواريخ (t=0)
إحداثيا متجهة سرعة القذيفة في لحظة t>0: