---
title: "A ship moves horizontally to the right at a constant speed \\(v_{\\text{ship}}\\rangle\\) relative to the water. A runner on the flat deck of the ship moves horizontally to the right at a constant speed \\(v_{\\text{runner}}\\rangle\\) relative to the ship. The runner tosses a small ball vertically upward relative to themself with an initial vertical speed \\(v_y\\). A deckhand standing motionless on the ship deck observes the motion of the ball. Air resistance is negligible. Which of the following claims correctly compares the maximum height \\(h\\) above the deck reached by the ball and the total time of flight \\(T\\) as measured by the runner and the deckhand, with the correct justification?"
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url: "https://nerd-notes.com/ubq/119086/"
date_modified: "2026-08-18T04:48:47+00:00"
---

# A ship moves horizontally to the right at a constant speed \(v_{\text{ship}}\rangle\) relative to the water. A runner on the flat deck of the ship moves horizontally to the right at a constant speed \(v_{\text{runner}}\rangle\) relative to the ship. The runner tosses a small ball vertically upward relative to themself with an initial vertical speed \(v_y\). A deckhand standing motionless on the ship deck observes the motion of the ball. Air resistance is negligible. Which of the following claims correctly compares the maximum height \(h\) above the deck reached by the ball and the total time of flight \(T\) as measured by the runner and the deckhand, with the correct justification?

A ship moves horizontally to the right at a constant speed \(v_{\text{ship}}\rangle\) relative to the water. A runner on the flat deck of the ship moves horizontally to the right at a constant speed \(v_{\text{runner}}\rangle\) relative to the ship. The runner tosses a small ball vertically upward relative to themself with an initial vertical speed \(v_y\). A deckhand standing motionless on the ship deck observes the motion of the ball. Air resistance is negligible. Which of the following claims correctly compares the maximum height \(h\) above the deck reached by the ball and the total time of flight \(T\) as measured by the runner and the deckhand, with the correct justification?

![A flat horizontal deck of a ship with a runner moving to the right and tossing a ball vertically upward. A deckhand stands still on the deck to the left. A vertical dashed line above the runner shows the straight vertical path of the ball, while a curved parabolic dashed path shows the motion relative to the deckhand. A horizontal vector arrow below the ship hull points rightward labeled v_{ship}. A horizontal vector arrow near the runner points rightward labeled v_{runner}. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787028526-81vSaa.jpg)

- **A.** \(h\) and \(T\) are both greater as measured by the deckhand because the ball has a greater initial speed relative to the deckhand.
- **B.** \(h\) is the same for both observers, but \(T\) is greater as measured by the deckhand because the ball follows a longer parabolic trajectory relative to the deckhand.
- **C.** Both \(h\) and \(T\) are the same for both observers because the initial vertical velocity component and the vertical acceleration of the ball are identical in both reference frames.
- **D.** \(h\) is greater as measured by the deckhand because the ball has horizontal kinetic energy that contributes to its peak height, but \(T\) is the same for both observers.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119086/*