---
title: "A small projectile of mass \\(m\\) travels horizontally with initial speed \\(v_0\\) toward a stationary block of mass \\(M\\) on a frictionless horizontal surface. The projectile strikes and becomes completely embedded inside the block. Let \\(K_i\\) and \\(p_i\\) represent the initial kinetic energy and initial linear momentum of the projectile, respectively. Let \\(|\\Delta K|\\) represent the magnitude of the mechanical kinetic energy dissipated during the collision, and let \\(J\\) represent the magnitude of the impulse delivered to the block of mass \\(M\\). In the limit as the mass ratio \\(\\dfrac{m}{M} \\to 0\\), what do the ratios \\(\\dfrac{|\\Delta K|}{K_i}\\) and \\(\\dfrac{J}{p_i}\\) approach?"
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url: "https://nerd-notes.com/ubq/120755/"
date_modified: "2026-08-23T04:43:01+00:00"
---

# A small projectile of mass \(m\) travels horizontally with initial speed \(v_0\) toward a stationary block of mass \(M\) on a frictionless horizontal surface. The projectile strikes and becomes completely embedded inside the block. Let \(K_i\) and \(p_i\) represent the initial kinetic energy and initial linear momentum of the projectile, respectively. Let \(|\Delta K|\) represent the magnitude of the mechanical kinetic energy dissipated during the collision, and let \(J\) represent the magnitude of the impulse delivered to the block of mass \(M\). In the limit as the mass ratio \(\dfrac{m}{M} \to 0\), what do the ratios \(\dfrac{|\Delta K|}{K_i}\) and \(\dfrac{J}{p_i}\) approach?

A small projectile of mass \(m\) travels horizontally with initial speed \(v_0\) toward a stationary block of mass \(M\) on a frictionless horizontal surface. The projectile strikes and becomes completely embedded inside the block. Let \(K_i\) and \(p_i\) represent the initial kinetic energy and initial linear momentum of the projectile, respectively. Let \(|\Delta K|\) represent the magnitude of the mechanical kinetic energy dissipated during the collision, and let \(J\) represent the magnitude of the impulse delivered to the block of mass \(M\). In the limit as the mass ratio \(\dfrac{m}{M} \to 0\), what do the ratios \(\dfrac{|\Delta K|}{K_i}\) and \(\dfrac{J}{p_i}\) approach?

![A horizontal line represents a frictionless floor. On the right sits a large rectangular block labeled M with height equal to width. To the left of the block, a small solid circle labeled m is depicted with a horizontal rightward arrow labeled v_0 pointing directly toward the center of the block. A dashed horizontal centerline aligns the path of the small mass with the center of the rectangular block. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460180-TdNzop.jpg)

- **A.** \(\dfrac{|\Delta K|}{K_i} \to 0\) and \(\dfrac{J}{p_i} \to 0\)
- **B.** \(\dfrac{|\Delta K|}{K_i} \to 0\) and \(\dfrac{J}{p_i} \to 1\)
- **C.** \(\dfrac{|\Delta K|}{K_i} \to 1\) and \(\dfrac{J}{p_i} \to 1\)
- **D.** \(\dfrac{|\Delta K|}{K_i} \to 1\) and \(\dfrac{J}{p_i} \to 0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120755/*