---
title: "A student performs an experiment to determine the acceleration due to gravity \\(g\\) by launching a small marble horizontally from the edge of a table with a constant initial speed \\(v_0\\). The student varies the height \\(H\\) of the table for several trials and measures the horizontal range \\(D\\) from the base of the table to the landing point on the floor. Which of the following pairs of quantities should be plotted to produce a linear graph, and what is the physical meaning of the slope of that graph?"
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url: "https://nerd-notes.com/ubq/110117/"
date_modified: "2026-08-11T08:35:58+00:00"
---

# A student performs an experiment to determine the acceleration due to gravity \(g\) by launching a small marble horizontally from the edge of a table with a constant initial speed \(v_0\). The student varies the height \(H\) of the table for several trials and measures the horizontal range \(D\) from the base of the table to the landing point on the floor. Which of the following pairs of quantities should be plotted to produce a linear graph, and what is the physical meaning of the slope of that graph?

A student performs an experiment to determine the acceleration due to gravity \(g\) by launching a small marble horizontally from the edge of a table with a constant initial speed \(v_0\). The student varies the height \(H\) of the table for several trials and measures the horizontal range \(D\) from the base of the table to the landing point on the floor. Which of the following pairs of quantities should be plotted to produce a linear graph, and what is the physical meaning of the slope of that graph?

![A horizontal tabletop of height H is shown with a marble at the right edge. The marble has a horizontal velocity vector v_0 pointing to the right. A dashed line represents the parabolic trajectory of the marble until it hits the level floor. The horizontal distance from the table edge to the impact point is labeled D. The vertical height from the floor to the tabletop is labeled H.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774589215-RUefdq.jpg)

- **A.** Plot \(D^2\) on the vertical axis and \(H\) on the horizontal axis; the slope is \(\dfrac{2v_0^2}{g}\).
- **B.** Plot \(D^2\) on the vertical axis and \(H\) on the horizontal axis; the slope is \(\dfrac{v_0^2}{2g}\).
- **C.** Plot \(H\) on the vertical axis and \(D^2\) on the horizontal axis; the slope is \(\dfrac{2g}{v_0^2}\).
- **D.** Plot \(H\) on the vertical axis and \(D^2\) on the horizontal axis; the slope is \(\dfrac{g}{v_0^2}\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/110117/*