---
title: "A cart of mass \\(M\\) is initially at rest on a horizontal, frictionless track. A launcher mounted on the cart fires a projectile of mass \\(m\\) with a speed \\(v_0\\) relative to the launcher at an angle \\(\\theta\\) above the horizontal. What is the speed of the cart immediately after the projectile is launched?"
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url: "https://nerd-notes.com/ubq/120720/"
date_modified: "2026-08-23T04:42:50+00:00"
---

# A cart of mass \(M\) is initially at rest on a horizontal, frictionless track. A launcher mounted on the cart fires a projectile of mass \(m\) with a speed \(v_0\) relative to the launcher at an angle \(\theta\) above the horizontal. What is the speed of the cart immediately after the projectile is launched?

A cart of mass \(M\) is initially at rest on a horizontal, frictionless track. A launcher mounted on the cart fires a projectile of mass \(m\) with a speed \(v_0\) relative to the launcher at an angle \(\theta\) above the horizontal. What is the speed of the cart immediately after the projectile is launched?

![A horizontal line represents a frictionless track. Resting on the track is a rectangular cart labeled \(M\) with two small circular wheels at the bottom touching the track. Mounted atop the cart is a cylindrical launcher tube inclined upward and to the right at an angle \(\theta\) above the horizontal surface of the cart. An arc with the label \(\theta\) indicates the launch angle between the launcher tube and the horizontal top edge of the cart. A small circular projectile labeled \(m\) is shown emerging from the mouth of the tube with a straight arrow pointing along the tube axis labeled \(v_0\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460170-xZ437U.jpg)

- **A.** \(\dfrac{m v_0 \cos\theta}{M}\)
- **B.** \(\dfrac{m v_0 \sin\theta}{M + m}\)
- **C.** \(\dfrac{m v_0 \cos\theta}{M + m}\)
- **D.** \(\dfrac{M v_0 \cos\theta}{M + m}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120720/*