---
title: "Ball 1 is released from rest from a balcony at a height \\(H\\) above the ground. At the same instant, Ball 2 is launched vertically upward from the ground with an initial speed \\(v_0\\). The balls pass each other at a height of \\(H/4\\) above the ground. Neglecting air resistance, which of the following is a correct expression for the initial speed \\(v_0\\) in terms of \\(H\\) and the acceleration due to gravity \\(g\\)?"
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url: "https://nerd-notes.com/ubq/113955/"
date_modified: "2026-06-22T07:38:47+00:00"
---

# Ball 1 is released from rest from a balcony at a height \(H\) above the ground. At the same instant, Ball 2 is launched vertically upward from the ground with an initial speed \(v_0\). The balls pass each other at a height of \(H/4\) above the ground. Neglecting air resistance, which of the following is a correct expression for the initial speed \(v_0\) in terms of \(H\) and the acceleration due to gravity \(g\)?

Ball 1 is released from rest from a balcony at a height \(H\) above the ground. At the same instant, Ball 2 is launched vertically upward from the ground with an initial speed \(v_0\). The balls pass each other at a height of \(H/4\) above the ground. Neglecting air resistance, which of the following is a correct expression for the initial speed \(v_0\) in terms of \(H\) and the acceleration due to gravity \(g\)?

![A vertical y-axis is shown. A circle representing Ball 1 is at the top at height H with a small arrow pointing downward. A circle representing Ball 2 is at the origin (ground, height 0) with a longer arrow pointing upward. A horizontal dashed line intersects the y-axis at a level labeled H/4. The vertical distance from the ground to the dashed line is visually one-fourth the distance from the ground to height H.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1782113926-L8lvuI.jpg)

- **A.** \(\sqrt{gH}\)
- **B.** \(\sqrt{\dfrac{2gH}{3}}\)
- **C.** \(\sqrt{\dfrac{3gH}{2}}\)
- **D.** \(\sqrt{2gH}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/113955/*