---
title: "An experiment is designed to determine the unknown mass \\(M\\) of a projectile that moves along a frictionless horizontal track. In each trial, the projectile travels at initial speed \\(v_i\\), strikes a fixed barrier, and rebounds in the opposite direction at speed \\(v_f\\). A sensor on the barrier measures the contact force \\(F(t)\\) over the collision duration \\(\\Delta t\\), and software computes the magnitude of the impulse \\(J = \\int_0^{\\Delta t} F(t)\\,dt\\). Which of the following pairs of quantities, when plotted on the vertical and horizontal axes, will produce a linear graph whose best-fit slope is directly equal to \\(M\\)?"
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url: "https://nerd-notes.com/ubq/120696/"
date_modified: "2026-08-23T04:42:43+00:00"
---

# An experiment is designed to determine the unknown mass \(M\) of a projectile that moves along a frictionless horizontal track. In each trial, the projectile travels at initial speed \(v_i\), strikes a fixed barrier, and rebounds in the opposite direction at speed \(v_f\). A sensor on the barrier measures the contact force \(F(t)\) over the collision duration \(\Delta t\), and software computes the magnitude of the impulse \(J = \int_0^{\Delta t} F(t)\,dt\). Which of the following pairs of quantities, when plotted on the vertical and horizontal axes, will produce a linear graph whose best-fit slope is directly equal to \(M\)?

An experiment is designed to determine the unknown mass \(M\) of a projectile that moves along a frictionless horizontal track. In each trial, the projectile travels at initial speed \(v_i\), strikes a fixed barrier, and rebounds in the opposite direction at speed \(v_f\). A sensor on the barrier measures the contact force \(F(t)\) over the collision duration \(\Delta t\), and software computes the magnitude of the impulse \(J = \int_0^{\Delta t} F(t)\,dt\). Which of the following pairs of quantities, when plotted on the vertical and horizontal axes, will produce a linear graph whose best-fit slope is directly equal to \(M\)?

- **A.** Vertical axis: \(J\); Horizontal axis: \(v_i + v_f\)
- **B.** Vertical axis: \(J\); Horizontal axis: \(v_i - v_f\)
- **C.** Vertical axis: \(J\); Horizontal axis: \(v_i^2 - v_f^2\)
- **D.** Vertical axis: \(v_i + v_f\); Horizontal axis: \(J\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120696/*