---
title: "A small bead slides without friction along the interior surface of a smooth, hollow inverted cone whose apex is pointed downward. The interior wall of the cone makes an angle of \\(45^\\circ\\) with its vertical central axis. The bead is launched horizontally along the wall at an initial height of \\(z_0 = 0.60 \\text{ m}\\) above the apex with a tangential speed of \\(v_0 = 1.0 \\text{ m/s}\\). What is the minimum vertical height above the apex reached by the bead during its motion?"
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url: "https://nerd-notes.com/ubq/124410/"
date_modified: "2026-09-28T14:05:14+00:00"
---

# A small bead slides without friction along the interior surface of a smooth, hollow inverted cone whose apex is pointed downward. The interior wall of the cone makes an angle of \(45^\circ\) with its vertical central axis. The bead is launched horizontally along the wall at an initial height of \(z_0 = 0.60 \text{ m}\) above the apex with a tangential speed of \(v_0 = 1.0 \text{ m/s}\). What is the minimum vertical height above the apex reached by the bead during its motion?

A small bead slides without friction along the interior surface of a smooth, hollow inverted cone whose apex is pointed downward. The interior wall of the cone makes an angle of \(45^\circ\) with its vertical central axis. The bead is launched horizontally along the wall at an initial height of \(z_0 = 0.60 \text{ m}\) above the apex with a tangential speed of \(v_0 = 1.0 \text{ m/s}\). What is the minimum vertical height above the apex reached by the bead during its motion?

![An inverted right circular cone oriented vertically with its sharp apex pointing downward at the origin. A vertical dashed line represents the central axis of symmetry rising from the apex. The cone walls extend upward and outward symmetrically, with an arc indicating an interior angle of 45 degrees between the vertical dashed axis and the right cone wall. A small solid circular dot representing a bead is positioned on the inner wall at an initial height labeled z_0, which corresponds to a horizontal radius labeled r_0 from the central axis. A horizontal arrow tangent to the cone's circumference at the bead's position indicates the initial horizontal velocity vector, labeled v_0. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604314-2pK2i3.jpg)

- **A.** \(0.05 \text{ m}\)
- **B.** \(0.10 \text{ m}\)
- **C.** \(0.15 \text{ m}\)
- **D.** \(0.20 \text{ m}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124410/*