---
title: "An athlete executes a high jump over a horizontal crossbar. During free flight, the only external force acting on the athlete is gravity, and air resistance is negligible. To clear the bar, the athlete dynamically arches their body so that their torso’s vertical displacement relative to their center of mass reaches a maximum at the peak of the jump. Which of the following correctly describes the qualitative shapes of the trajectory curves, \\(y(x)\\), and compares the magnitudes of their curvatures at the apex for the athlete’s center of mass and torso?"
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/124257/"
date_modified: "2026-09-28T14:04:33+00:00"
---

# An athlete executes a high jump over a horizontal crossbar. During free flight, the only external force acting on the athlete is gravity, and air resistance is negligible. To clear the bar, the athlete dynamically arches their body so that their torso’s vertical displacement relative to their center of mass reaches a maximum at the peak of the jump. Which of the following correctly describes the qualitative shapes of the trajectory curves, \(y(x)\), and compares the magnitudes of their curvatures at the apex for the athlete’s center of mass and torso?

An athlete executes a high jump over a horizontal crossbar. During free flight, the only external force acting on the athlete is gravity, and air resistance is negligible. To clear the bar, the athlete dynamically arches their body so that their torso's vertical displacement relative to their center of mass reaches a maximum at the peak of the jump. Which of the following correctly describes the qualitative shapes of the trajectory curves, \(y(x)\), and compares the magnitudes of their curvatures at the apex for the athlete's center of mass and torso?

- **A.** Both the center of mass and the torso follow strictly parabolic paths, and both curves have the same curvature at their respective peaks.
- **B.** The center of mass follows a strictly parabolic path, whereas the torso follows a non-parabolic path whose curvature at the apex is less than that of the center of mass.
- **C.** The center of mass follows a strictly parabolic path, whereas the torso follows a non-parabolic path whose curvature at the apex is greater than that of the center of mass.
- **D.** The center of mass follows a non-parabolic path due to the shifting mass distribution, whereas the torso follows a strictly parabolic path with curvature \(\dfrac{g}{v_x^2}\) at its apex.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124257/*