---
title: "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?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/120504/"
date_modified: "2026-08-23T04:39:15+00:00"
---

# 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?

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?

![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.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459955-sph1ND.jpg)

- **A.** \(\dfrac{v_0^2}{g}\)
- **B.** \(\dfrac{v_0^2 \sin^2\theta}{2g}\)
- **C.** \(\dfrac{v_0^2 \cos^2\theta}{g}\)
- **D.** \(\dfrac{v_0^2}{g \cos\theta}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120504/*