---
title: "A projectile is launched from level ground with an initial speed \\(v_0\\) at an angle \\(\\theta\\) above the horizontal. During its motion, the projectile reaches a height \\(h\\) above the ground at two different horizontal positions, \\(x = d_1\\) and \\(x = d_2\\), as measured from the launch point. Which of the following expressions represents the total horizontal range \\(R\\) of the projectile in terms of \\(d_1\\) and \\(d_2\\)?"
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/113070/"
date_modified: "2026-05-05T03:45:34+00:00"
---

# A projectile is launched from level ground with an initial speed \(v_0\) at an angle \(\theta\) above the horizontal. During its motion, the projectile reaches a height \(h\) above the ground at two different horizontal positions, \(x = d_1\) and \(x = d_2\), as measured from the launch point. Which of the following expressions represents the total horizontal range \(R\) of the projectile in terms of \(d_1\) and \(d_2\)?

A projectile is launched from level ground with an initial speed \(v_0\) at an angle \(\theta\) above the horizontal. During its motion, the projectile reaches a height \(h\) above the ground at two different horizontal positions, \(x = d_1\) and \(x = d_2\), as measured from the launch point. Which of the following expressions represents the total horizontal range \(R\) of the projectile in terms of \(d_1\) and \(d_2\)?

![A parabolic trajectory of a projectile launched from the origin (0,0). A horizontal dashed line at height h intersects the parabola at two points. The first point is at horizontal position d1 and the second point is at horizontal position d2. The projectile eventually lands on the x-axis at distance R.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1777952733-nHwfYd.jpg)

- **A.** \(d_2 - d_1\)
- **B.** \(d_1 + d_2\)
- **C.** \(2(d_2 - d_1)\)
- **D.** \(\sqrt{d_1 d_2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/113070/*