---
title: "A passenger on a flatcar of a train moving at a constant horizontal velocity \\(v_x\\) throws a ball straight up relative to the train. An observer standing on the ground sees the ball follow a parabolic path. At the instant the ball reaches its maximum height relative to the ground, which of the following correctly describes the magnitude of the ball’s acceleration, \\(a\\), and the rate at which the ball’s speed is changing, \\(\\dfrac{dv}{dt}\\)?"
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url: "https://nerd-notes.com/ubq/113947/"
date_modified: "2026-06-22T07:38:39+00:00"
---

# A passenger on a flatcar of a train moving at a constant horizontal velocity \(v_x\) throws a ball straight up relative to the train. An observer standing on the ground sees the ball follow a parabolic path. At the instant the ball reaches its maximum height relative to the ground, which of the following correctly describes the magnitude of the ball’s acceleration, \(a\), and the rate at which the ball’s speed is changing, \(\dfrac{dv}{dt}\)?

A passenger on a flatcar of a train moving at a constant horizontal velocity \(v_x\) throws a ball straight up relative to the train. An observer standing on the ground sees the ball follow a parabolic path. At the instant the ball reaches its maximum height relative to the ground, which of the following correctly describes the magnitude of the ball's acceleration, \(a\), and the rate at which the ball's speed is changing, \(\dfrac{dv}{dt}\)?

![A dashed parabolic trajectory of a projectile moving from left to right. At the highest point (the vertex), there is a horizontal vector arrow pointing to the right labeled 'v' and a vertical vector arrow pointing straight down labeled 'g'. A right-angle symbol is drawn between the two vectors.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/projectile-peak-diagram-1782113919-RlEJRC.jpg)

- **A.** \(a = g\) and \(\dfrac{dv}{dt} = g\), because the ball is under the influence of a constant gravitational force.
- **B.** \(a = g\) and \(\dfrac{dv}{dt} = 0\), because the acceleration is perpendicular to the velocity at that instant.
- **C.** \(a = 0\) and \(\dfrac{dv}{dt} = 0\), because the ball has reached its highest point and has no vertical velocity.
- **D.** \(a = 0\) and \(\dfrac{dv}{dt} = g\), because the horizontal motion is constant but the vertical motion is reversing direction.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/113947/*