---
title: "A projectile is launched over level ground with an initial speed \\(v_0\\) at an angle \\(\\theta_0\\) above the horizontal, where \\(0^\\circ < \\theta_0 < 90^\\circ\\). Air resistance is negligible, and the acceleration due to gravity has magnitude \\(g\\). At the apogee of its trajectory, what are the magnitude of the projectile's tangential acceleration, \\(a_t\\), and the magnitude of its normal acceleration, \\(a_n\\)?"
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url: "https://nerd-notes.com/ubq/124110/"
date_modified: "2026-09-28T13:30:28+00:00"
---

# A projectile is launched over level ground with an initial speed \(v_0\) at an angle \(\theta_0\) above the horizontal, where \(0^\circ < \theta_0 < 90^\circ\). Air resistance is negligible, and the acceleration due to gravity has magnitude \(g\). At the apogee of its trajectory, what are the magnitude of the projectile's tangential acceleration, \(a_t\), and the magnitude of its normal acceleration, \(a_n\)?

A projectile is launched over level ground with an initial speed \(v_0\) at an angle \(\theta_0\) above the horizontal, where \(0^\circ < \theta_0 < 90^\circ\). Air resistance is negligible, and the acceleration due to gravity has magnitude \(g\). At the apogee of its trajectory, what are the magnitude of the projectile's tangential acceleration, \(a_t\), and the magnitude of its normal acceleration, \(a_n\)?

![A horizontal solid line represents level ground with an origin labeled with a small open circle. From the origin, a solid curved parabolic trajectory opens downward, rising to a peak and descending symmetrically back to the ground. A single straight arrow points tangentially along the curve at the origin toward the upper-right at an angle labeled \(\theta_0\), with a label \(\vec{v}_0\) near the arrowhead. At the highest point of the parabolic curve, a single solid dot marks the apogee. Directly above this dot, the word Apogee is displayed in plain text. A vertical downward arrow labeled \(\vec{g}\) is placed to the right of the trajectory in open space. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602228-P3F75F.jpg)

- **A.** \(a_t = g\) and \(a_n = 0\)
- **B.** \(a_t = 0\) and \(a_n = g\)
- **C.** \(a_t = g\) and \(a_n = g\)
- **D.** \(a_t = 0\) and \(a_n = 0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124110/*