---
title: "Four identical projectiles, P, Q, R, and S, are launched simultaneously from the edge of a vertical cliff of height H above a flat horizontal plain with negligible air resistance.  | Projectile | Horizontal velocity component (\\(v_x\\)) | Vertical velocity component (\\(v_y\\)) | | :—: | :—: | :—: | | P | \\(2v_0\\) | \\(+v_0\\) | | Q | \\(v_0\\) | \\(+2v_0\\) | | R | \\(2v_0\\) | \\(-v_0\\) | | S | \\(v_0\\) | \\(0\\) |  The table lists the initial velocity components for each projectile, where the \\(+x\\)-direction is directed horizontally away from the cliff face and the \\(+y\\)-direction is directed vertically upward. Which of the following correctly ranks the times of flight, \\(\\Delta t\\), of the projectiles from launch until they strike the plain?"
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url: "https://nerd-notes.com/ubq/124010/"
date_modified: "2026-09-28T13:30:11+00:00"
---

# Four identical projectiles, P, Q, R, and S, are launched simultaneously from the edge of a vertical cliff of height H above a flat horizontal plain with negligible air resistance.

| Projectile | Horizontal velocity component (\(v_x\)) | Vertical velocity component (\(v_y\)) |
| :—: | :—: | :—: |
| P | \(2v_0\) | \(+v_0\) |
| Q | \(v_0\) | \(+2v_0\) |
| R | \(2v_0\) | \(-v_0\) |
| S | \(v_0\) | \(0\) |

The table lists the initial velocity components for each projectile, where the \(+x\)-direction is directed horizontally away from the cliff face and the \(+y\)-direction is directed vertically upward. Which of the following correctly ranks the times of flight, \(\Delta t\), of the projectiles from launch until they strike the plain?

Four identical projectiles, P, Q, R, and S, are launched simultaneously from the edge of a vertical cliff of height H above a flat horizontal plain with negligible air resistance.

| Projectile | Horizontal velocity component (\(v_x\)) | Vertical velocity component (\(v_y\)) |
| :---: | :---: | :---: |
| P | \(2v_0\) | \(+v_0\) |
| Q | \(v_0\) | \(+2v_0\) |
| R | \(2v_0\) | \(-v_0\) |
| S | \(v_0\) | \(0\) |

The table lists the initial velocity components for each projectile, where the \(+x\)-direction is directed horizontally away from the cliff face and the \(+y\)-direction is directed vertically upward. Which of the following correctly ranks the times of flight, \(\Delta t\), of the projectiles from launch until they strike the plain?

![A high vertical cliff face with flat horizontal ground at its base and a flat horizontal surface at its top. At the top edge of the cliff, a single launch point shows four distinct velocity vector arrows originating from the same point, each labeled with a projectile letter. Arrow P points upward and rightward at a moderate angle above the horizontal. Arrow Q points steeply upward and slightly rightward. Arrow R points downward and rightward at an angle below the horizontal. Arrow S points horizontally to the right. A vertical dashed dimension line spans the vertical height of the cliff and is labeled H. A coordinate axis indicator in the upper-left corner shows a horizontal arrow labeled +x pointing right and a vertical arrow labeled +y pointing up. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602211-sgwMAB.jpg)

- **A.** \(\Delta t_Q > \Delta t_P > \Delta t_S > \Delta t_R\)
- **B.** \(\Delta t_P = \Delta t_Q = \Delta t_R > \Delta t_S\)
- **C.** \(\Delta t_Q > \Delta t_P = \Delta t_R > \Delta t_S\)
- **D.** \(\Delta t_P > \Delta t_Q > \Delta t_S > \Delta t_R\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124010/*