---
title: "At time \\(t = 0\\), Sphere 1 is released from rest from the edge of a horizontal cliff of height \\(H\\) above flat ground. At the exact same instant, an identical Sphere 2 is launched horizontally from the same height with an initial speed \\(v_0\\). Air resistance is negligible. Which of the following correctly compares the time of flight \\(t_1\\) of Sphere 1 to the time of flight \\(t_2\\) of Sphere 2, and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/120483/"
date_modified: "2026-08-23T04:39:06+00:00"
---

# At time \(t = 0\), Sphere 1 is released from rest from the edge of a horizontal cliff of height \(H\) above flat ground. At the exact same instant, an identical Sphere 2 is launched horizontally from the same height with an initial speed \(v_0\). Air resistance is negligible. Which of the following correctly compares the time of flight \(t_1\) of Sphere 1 to the time of flight \(t_2\) of Sphere 2, and provides the correct physical justification?

At time \(t = 0\), Sphere 1 is released from rest from the edge of a horizontal cliff of height \(H\) above flat ground. At the exact same instant, an identical Sphere 2 is launched horizontally from the same height with an initial speed \(v_0\). Air resistance is negligible. Which of the following correctly compares the time of flight \(t_1\) of Sphere 1 to the time of flight \(t_2\) of Sphere 2, and provides the correct physical justification?

![A horizontal cliff of height \(H\) is shown above a flat horizontal ground line. At the upper right edge of the cliff, Sphere 1 and Sphere 2 are positioned side-by-side at the same elevation. A downward vertical dashed line with a downward-pointing arrowhead extends from Sphere 1 to the ground directly below. A horizontal solid vector arrow labeled \(v_0\) points to the right from Sphere 2, and a smooth downward-curving parabolic dashed line extends from Sphere 2 to the ground further to the right. A vertical dimension line with arrowheads at both ends is placed along the cliff face and labeled \(H\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459945-hU8aDs.jpg)

- **A.** \(t_1 < t_2\), because Sphere 2 travels a longer curved path to the ground under the same downward gravitational acceleration.
- **B.** \(t_1 > t_2\), because Sphere 2 has a greater total initial velocity, leading to a larger average speed toward the ground during its flight.
- **C.** \(t_1 = t_2\), because perpendicular components of motion are independent, and both spheres start with zero initial vertical velocity and undergo identical vertical acceleration.
- **D.** \(t_1 = t_2\), because gravity does equal work on both spheres over the vertical displacement \(H\), ensuring that the time taken to reach the ground must be equal.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120483/*