---
title: "A cart of mass \\(M\\) carries two runners, each of mass \\(m\\), and is initially at rest on a frictionless horizontal track. If both runners jump off opposite ends of the cart simultaneously with identical horizontal speed \\(u\\) relative to the cart, the cart remains at rest. However, if the first runner jumps to the left with speed \\(u\\) relative to the cart, and subsequently the second runner jumps to the right with speed \\(u\\) relative to the cart, the cart acquires a non-zero final velocity directed to the left. Which of the following statements best explains why the cart moves to the left following the sequential jumps?"
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/124272/"
date_modified: "2026-09-28T14:04:37+00:00"
---

# A cart of mass \(M\) carries two runners, each of mass \(m\), and is initially at rest on a frictionless horizontal track. If both runners jump off opposite ends of the cart simultaneously with identical horizontal speed \(u\) relative to the cart, the cart remains at rest. However, if the first runner jumps to the left with speed \(u\) relative to the cart, and subsequently the second runner jumps to the right with speed \(u\) relative to the cart, the cart acquires a non-zero final velocity directed to the left. Which of the following statements best explains why the cart moves to the left following the sequential jumps?

A cart of mass \(M\) carries two runners, each of mass \(m\), and is initially at rest on a frictionless horizontal track. If both runners jump off opposite ends of the cart simultaneously with identical horizontal speed \(u\) relative to the cart, the cart remains at rest. However, if the first runner jumps to the left with speed \(u\) relative to the cart, and subsequently the second runner jumps to the right with speed \(u\) relative to the cart, the cart acquires a non-zero final velocity directed to the left. Which of the following statements best explains why the cart moves to the left following the sequential jumps?

![A horizontal straight line represents a frictionless track. Resting on the track is a wide rectangular cart labeled M supported by four small circular wheels. Standing on the left side of the cart is a stick figure labeled m facing to the left with an arrow pointing left labeled u. Standing on the right side of the cart is an identical stick figure labeled m facing to the right with an arrow pointing right labeled u. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604277-j5IIpw.jpg)

- **A.** Between the two jumps, the center of mass of the isolated system drifts to the right, requiring the cart to acquire a leftward velocity after the second jump so that the center of mass eventually returns to its starting location.
- **B.** Because the cart is already moving rightward when the second runner jumps, the contact duration between the runner and the cart is extended, thereby delivering a significantly larger leftward impulse to the cart.
- **C.** The second runner must perform more muscular work in the ground frame to achieve the relative launch speed \(u\) from a moving cart, and this greater energy expenditure directly produces a larger recoil velocity.
- **D.** During the second jump, the total mass of the remaining system is smaller than it was during the first jump, so ejecting the runner at relative speed \(u\) produces a leftward velocity change of greater magnitude than the initial rightward change.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124272/*