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title: "A scout aircraft maneuvers in a horizontal plane with a position vector as a function of time given by \\(\\vec{r}_S(t) = R\\cos(\\omega t)\\hat{i} + R\\sin(\\omega t)\\hat{j}\\), where \\(R\\) and \\(\\omega\\) are positive constants, and \\(v_0 = R\\omega\\). At time \\(t = \\dfrac{\\pi}{2\\omega}\\), four target drones have constant velocities relative to the ground: Drone 1 has velocity \\(v_0\\hat{i}\\), Drone 2 has velocity \\(-v_0\\hat{i}\\), Drone 3 has velocity \\(v_0\\hat{j}\\), and Drone 4 has velocity \\(2v_0\\hat{i}\\). Which of the following correctly ranks the speeds of the four drones as measured by an observer on the scout aircraft at this instant, from greatest to least?"
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url: "https://nerd-notes.com/ubq/124161/"
date_modified: "2026-09-28T13:30:51+00:00"
---

# A scout aircraft maneuvers in a horizontal plane with a position vector as a function of time given by \(\vec{r}_S(t) = R\cos(\omega t)\hat{i} + R\sin(\omega t)\hat{j}\), where \(R\) and \(\omega\) are positive constants, and \(v_0 = R\omega\). At time \(t = \dfrac{\pi}{2\omega}\), four target drones have constant velocities relative to the ground: Drone 1 has velocity \(v_0\hat{i}\), Drone 2 has velocity \(-v_0\hat{i}\), Drone 3 has velocity \(v_0\hat{j}\), and Drone 4 has velocity \(2v_0\hat{i}\). Which of the following correctly ranks the speeds of the four drones as measured by an observer on the scout aircraft at this instant, from greatest to least?

A scout aircraft maneuvers in a horizontal plane with a position vector as a function of time given by \(\vec{r}_S(t) = R\cos(\omega t)\hat{i} + R\sin(\omega t)\hat{j}\), where \(R\) and \(\omega\) are positive constants, and \(v_0 = R\omega\). At time \(t = \dfrac{\pi}{2\omega}\), four target drones have constant velocities relative to the ground: Drone 1 has velocity \(v_0\hat{i}\), Drone 2 has velocity \(-v_0\hat{i}\), Drone 3 has velocity \(v_0\hat{j}\), and Drone 4 has velocity \(2v_0\hat{i}\). Which of the following correctly ranks the speeds of the four drones as measured by an observer on the scout aircraft at this instant, from greatest to least?

- **A.** Drone 2 > Drone 3 > Drone 4 > Drone 1
- **B.** Drone 4 > Drone 2 > Drone 3 > Drone 1
- **C.** Drone 4 > Drone 1 > Drone 3 > Drone 2
- **D.** Drone 4 > Drone 3 > Drone 1 > Drone 2

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124161/*