---
title: "A projectile is launched from level ground with an initial speed \\( v_0 \\) at an angle \\( \\theta_1 \\) above the horizontal and has a horizontal range \\( R \\) and a maximum height \\( H_1 \\). A second projectile is launched from the same location with the same initial speed \\( v_0 \\) at an angle \\( \\theta_2 \\) above the horizontal and has the same horizontal range \\( R \\) but a maximum height \\( H_2 \\). If \\( \\theta_2 > \\theta_1 \\) and \\( H_2 = 3H_1 \\), what is the value of \\( \\theta_1 \\)?"
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url: "https://nerd-notes.com/ubq/109244/"
date_modified: "2026-03-21T18:07:41+00:00"
---

# A projectile is launched from level ground with an initial speed \( v_0 \) at an angle \( \theta_1 \) above the horizontal and has a horizontal range \( R \) and a maximum height \( H_1 \). A second projectile is launched from the same location with the same initial speed \( v_0 \) at an angle \( \theta_2 \) above the horizontal and has the same horizontal range \( R \) but a maximum height \( H_2 \). If \( \theta_2 > \theta_1 \) and \( H_2 = 3H_1 \), what is the value of \( \theta_1 \)?

A projectile is launched from level ground with an initial speed \( v_0 \) at an angle \( \theta_1 \) above the horizontal and has a horizontal range \( R \) and a maximum height \( H_1 \). A second projectile is launched from the same location with the same initial speed \( v_0 \) at an angle \( \theta_2 \) above the horizontal and has the same horizontal range \( R \) but a maximum height \( H_2 \). If \( \theta_2 > \theta_1 \) and \( H_2 = 3H_1 \), what is the value of \( \theta_1 \)?

![A graph showing two parabolic trajectories on a horizontal x-axis. Both paths start at the origin and end at the same point labeled R. The first path is lower with a maximum height labeled H1 and a launch angle labeled theta1. The second path is higher with a maximum height labeled H2 and a launch angle labeled theta2. Both launch vectors have the same length labeled v0.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774116460-rQFdhF.jpg)

- **A.** \( 15^{\circ} \)
- **B.** \( 30^{\circ} \)
- **C.** \( 45^{\circ} \)
- **D.** \( 60^{\circ} \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109244/*