---
title: "A projectile is launched from ground level toward a vertical barrier located at a horizontal distance d from the launch point. The top of the barrier is at a height h above the ground. Neglecting air resistance, what is the minimum launch speed v_{min} required for the projectile to clear the top of the barrier?"
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url: "https://nerd-notes.com/ubq/120498/"
date_modified: "2026-08-23T04:39:13+00:00"
---

# A projectile is launched from ground level toward a vertical barrier located at a horizontal distance d from the launch point. The top of the barrier is at a height h above the ground. Neglecting air resistance, what is the minimum launch speed v_{min} required for the projectile to clear the top of the barrier?

A projectile is launched from ground level toward a vertical barrier located at a horizontal distance d from the launch point. The top of the barrier is at a height h above the ground. Neglecting air resistance, what is the minimum launch speed v_{min} required for the projectile to clear the top of the barrier?

![A two-dimensional schematic on a white background showing a flat horizontal ground line. At the left end is a launch point labeled (0,0). At a horizontal distance d to the right stands a thin vertical line representing a barrier of height h. A horizontal double-headed dimension arrow below the ground line spans from the launch point to the base of the barrier, labeled d. A vertical double-headed dimension arrow to the right of the barrier spans from the ground to the top of the barrier, labeled h. A dashed parabolic curve originates at (0,0), rises smoothly, and passes just over the top tip of the barrier. An arrow tangent to the dashed curve at the origin points upward and to the right at an angle \theta above the horizontal, labeled v_0. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459953-DdYysk.jpg)

- **A.** \(\sqrt{g\left(h + \sqrt{d^2 + h^2}\right)}\)
- **B.** \(\sqrt{g\left(\sqrt{d^2 + h^2} - h\right)}\)
- **C.** \(\sqrt{g\left(d + \sqrt{d^2 + h^2}\right)}\)
- **D.** \(\sqrt{2g\left(h + \sqrt{d^2 + h^2}\right)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120498/*