---
title: "A student is calibrating a projectile launcher to be used in a laboratory experiment. The launcher is placed on the ground and set to fire a ball at an angle \\( 	heta \\) above the horizontal across a level field. In the first calibration trial, the ball is launched with an initial speed \\( v_0 \\) and travels a horizontal distance \\( D_1 \\) before hitting the ground. In the second calibration trial, the launcher is adjusted to fire the ball at the same angle \\( 	heta \\) but with an initial speed of \\( 2v_0 \\), resulting in a horizontal distance \\( D_2 \\). What is the ratio of the horizontal distance \\( D_2 \\) to the horizontal distance \\( D_1 \\)?"
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url: "https://nerd-notes.com/ubq/112347/"
date_modified: "2026-04-24T01:12:40+00:00"
---

# A student is calibrating a projectile launcher to be used in a laboratory experiment. The launcher is placed on the ground and set to fire a ball at an angle \( 	heta \) above the horizontal across a level field. In the first calibration trial, the ball is launched with an initial speed \( v_0 \) and travels a horizontal distance \( D_1 \) before hitting the ground. In the second calibration trial, the launcher is adjusted to fire the ball at the same angle \( 	heta \) but with an initial speed of \( 2v_0 \), resulting in a horizontal distance \( D_2 \). What is the ratio of the horizontal distance \( D_2 \) to the horizontal distance \( D_1 \)?

A student is calibrating a projectile launcher to be used in a laboratory experiment. The launcher is placed on the ground and set to fire a ball at an angle \( 	heta \) above the horizontal across a level field. In the first calibration trial, the ball is launched with an initial speed \( v_0 \) and travels a horizontal distance \( D_1 \) before hitting the ground. In the second calibration trial, the launcher is adjusted to fire the ball at the same angle \( 	heta \) but with an initial speed of \( 2v_0 \), resulting in a horizontal distance \( D_2 \). What is the ratio of the horizontal distance \( D_2 \) to the horizontal distance \( D_1 \)?

![A side-view diagram of a projectile launcher on a flat horizontal surface. A dotted parabolic path shows a ball launched at angle theta and landing a distance D1 away. A second, larger dotted parabolic path starts from the same point at the same angle theta but reaches a higher peak and lands much further away at distance D2.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1776993160-ibTNHu.jpg)

- **A.** \( 1:1 \)
- **B.** \( 2:1 \)
- **C.** \( 4:1 \)
- **D.** \( 8:1 \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/112347/*