---
title: "Two small spheres are launched horizontally from the edge of a cliff of height \\(H\\) above a level plain. Sphere 1 is launched with an initial horizontal velocity of magnitude \\(v_0\\), and Sphere 2 is launched with an initial horizontal velocity of magnitude \\(2v_0\\). Which of the following correctly compares the flight time \\(t_1\\) of Sphere 1 to the flight time \\(t_2\\) of Sphere 2 and provides a valid justification?"
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url: "https://nerd-notes.com/ubq/109242/"
date_modified: "2026-03-21T18:07:39+00:00"
---

# Two small spheres are launched horizontally from the edge of a cliff of height \(H\) above a level plain. Sphere 1 is launched with an initial horizontal velocity of magnitude \(v_0\), and Sphere 2 is launched with an initial horizontal velocity of magnitude \(2v_0\). Which of the following correctly compares the flight time \(t_1\) of Sphere 1 to the flight time \(t_2\) of Sphere 2 and provides a valid justification?

Two small spheres are launched horizontally from the edge of a cliff of height \(H\) above a level plain. Sphere 1 is launched with an initial horizontal velocity of magnitude \(v_0\), and Sphere 2 is launched with an initial horizontal velocity of magnitude \(2v_0\). Which of the following correctly compares the flight time \(t_1\) of Sphere 1 to the flight time \(t_2\) of Sphere 2 and provides a valid justification?

![A side-view diagram of a cliff. The top edge of the cliff is on the left, and it drops off to a level ground below. Two spheres, labeled 1 and 2, are at the edge. Sphere 1 has a short horizontal arrow labeled v_0. Sphere 2 has a horizontal arrow twice as long as the first, labeled 2v_0. Dotted parabolic paths show Sphere 1 landing at a horizontal distance x and Sphere 2 landing further away at 2x. A vertical dimension line indicates the height H from the ground to the cliff edge.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774116459-58GQuI.jpg)

- **A.** The flight times are equal (\(t_1 = t_2\)) because both spheres have the same initial vertical velocity and the same vertical acceleration.
- **B.** The flight times are equal (\(t_1 = t_2\)) because the horizontal velocity of each sphere remains constant throughout its flight.
- **C.** Sphere 2 is in the air for more time (\(t_2 > t_1\)) because it travels a greater total distance along its parabolic path to the ground.
- **D.** Sphere 2 is in the air for less time (\(t_2 < t_1\)) because its higher initial speed allows it to reach the ground more quickly.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109242/*