**Fireworks Rocket Motion Analysis****Problem Statement:**A fireworks rocket traveling at a speed of \(37.5 \, \text{m/s}\) suddenly breaks into two pieces of equal mass. If the masses fly off with velocities \(\vec{v}_1\) and \(\vec{v}_2\), as shown in the diagram, determine the speed of each mass.---**Diagram Explanation:**The diagram shows:- The initial velocity \( \vec{v}_0 \) of the fireworks rocket is horizontal at \(37.5 \, \text{m/s}\).- The rocket breaks into two pieces.- The first piece (labeled \(\vec{v}_1\)) moves upward at an angle of \(30.0^\circ\) to the horizontal.- The second piece (labeled \(\vec{v}_2\)) moves downward at an angle of \(60.0^\circ\) to the horizontal.---**Questions:**(a) Determine the speed associated with \(\vec{v}_1\) \[ \boxed{\phantom{000}} \, \text{m/s} \](b) Determine the speed associated with \(\vec{v}_2\) \[ \boxed{\phantom{000}} \, \text{m/s} \]---**Graphical Details:**- The initial motion of the rocket is displayed with a single arrow moving to the right.- After the explosion, two separate arrows representing \(\vec{v}_1\) and \(\vec{v}_2\) point away from the initial position.- \(\vec{v}_1\) is directed at \(30.0^\circ\) above the horizontal.- \(\vec{v}_2\) is directed at \(60.0^\circ\) below the horizontal.- Dashed lines indicate the angles between the velocities and the horizontal reference line.### Important Concepts for Solution:To solve for the velocities \(v_1\) and \(v_2\), conservation of momentum principles need to be applied both horizontally and vertically.\( \vec{v_1} \) and \( \vec{v_2} \) can be broken down into horizontal (\(v_{1x}\) and \(v_{2x}\)) and vertical (\(v_{1y}\) and \(v_{2y}\

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A fireworks rocket moving at a speed of 37.5 m/s suddenly breaks into two pieces of equal mass. If the masses fly off with velocities v, and v 2, as shown in the drawing, determine the speed of each mass.

A fireworks rocket moving at a speed of 37.5 m/s suddenly breaks into two pieces of equal mass. If the masses fly off with velocities v, and v 2, as shown in the drawing, determine the speed of each mass.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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**Fireworks Rocket Motion Analysis**

**Problem Statement:**
A fireworks rocket traveling at a speed of \(37.5 \, \text{m/s}\) suddenly breaks into two pieces of equal mass. If the masses fly off with velocities \(\vec{v}_1\) and \(\vec{v}_2\), as shown in the diagram, determine the speed of each mass.

---

**Diagram Explanation:**

The diagram shows:
- The initial velocity \( \vec{v}_0 \) of the fireworks rocket is horizontal at \(37.5 \, \text{m/s}\).
- The rocket breaks into two pieces.
- The first piece (labeled \(\vec{v}_1\)) moves upward at an angle of \(30.0^\circ\) to the horizontal.
- The second piece (labeled \(\vec{v}_2\)) moves downward at an angle of \(60.0^\circ\) to the horizontal.

---

**Questions:**

(a) Determine the speed associated with \(\vec{v}_1\)
\[ \boxed{\phantom{000}} \, \text{m/s} \]

(b) Determine the speed associated with \(\vec{v}_2\)
\[ \boxed{\phantom{000}} \, \text{m/s} \]

---

**Graphical Details:**

- The initial motion of the rocket is displayed with a single arrow moving to the right.
- After the explosion, two separate arrows representing \(\vec{v}_1\) and \(\vec{v}_2\) point away from the initial position.
- \(\vec{v}_1\) is directed at \(30.0^\circ\) above the horizontal.
- \(\vec{v}_2\) is directed at \(60.0^\circ\) below the horizontal.
- Dashed lines indicate the angles between the velocities and the horizontal reference line.

### Important Concepts for Solution:
To solve for the velocities \(v_1\) and \(v_2\), conservation of momentum principles need to be applied both horizontally and vertically.

\( \vec{v_1} \) and \( \vec{v_2} \) can be broken down into horizontal (\(v_{1x}\) and \(v_{2x}\)) and vertical (\(v_{1y}\) and \(v_{2y}\

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