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AP Physics C: Mechanics
1.5 Motion in Two or Three Dimensions
AdvancedMCQMathematical15.7k
A two-dimensional coordinate system with a horizontal x-axis and a vertical y-axis meeting at origin (0,0). A smooth, downward-opening parabolic dashed curve begins at (0,0) and ends at a point on the positive x-axis. At the origin (0,0), a solid arrow labeled \(v_0\) points up and to the right at an angle \(\theta\) above the horizontal x-axis, with a small curved arc indicating the angle \(\theta\). At the highest point of the parabolic curve, a small solid circular dot represents the projectile. A downward vertical arrow from the dot is labeled \(g\). No other labels, lines, text, or axes appear.
Trajectory of a projectile launched at angle \(\theta\) with speed \(v_0\).
A projectile is launched from horizontal ground with an initial speed \(v_0\) at an angle \(\theta\) above the horizontal, where \(0 < \theta < \dfrac{\pi}{2}\). Air resistance is negligible, and the acceleration due to gravity has constant magnitude \(g\). Which of the following expressions represents the instantaneous radius of curvature of the projectile's trajectory at the apex of its flight?

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