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Illustration Oblique Throw - Trajectory with Initial Velocity, Angle and Height

Oblique throw - trajectory with initial velocity, angle and height
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A body is dropped from height \(y_0\) with initial velocity \(v_0\) at an angle \(\varphi_0\). The body traverses a parabolic path and then lands at distance \(w\) from the launch point. To maximize the throw distance \(w\), the launch angle must be \( 45 ^{\circ} \).