An object of mass 3M, moving in the +x direction at speed o, breaks into two pieces of mass M and 2M as shown in the figure. If 0₁ = 64.0° and 9₂ ₁ and 2 of the resulting pieces in terms of Uo- - 20.0°, determine the final velocities

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An object of mass \(3M\), moving in the \(+x\) direction at speed \(v_0\), breaks into two pieces of mass \(M\) and \(2M\) as shown in the figure.

If \(\theta_1 = 64.0^\circ\) and \(\theta_2 = 20.0^\circ\), determine the final velocities \(v_1\) and \(v_2\) of the resulting pieces in terms of \(v_0\).

\[ 
v_1 = \_\_\_\_ \, v_0 
\]

\[ 
v_2 = \_\_\_\_ \, v_0 
\]

**Diagram Details:**

- The initial object of mass \(3M\) is represented by a blue sphere moving to the right with velocity \(v_0\).
- After the break, there are two smaller spheres:
  - The green sphere has a mass of \(2M\) and is moving at an unknown velocity \(v_2\) at an angle \(\theta_2 = 20.0^\circ\).
  - The orange sphere has a mass of \(M\) and is moving at an unknown velocity \(v_1\) at an angle \(\theta_1 = 64.0^\circ\).
Transcribed Image Text:An object of mass \(3M\), moving in the \(+x\) direction at speed \(v_0\), breaks into two pieces of mass \(M\) and \(2M\) as shown in the figure. If \(\theta_1 = 64.0^\circ\) and \(\theta_2 = 20.0^\circ\), determine the final velocities \(v_1\) and \(v_2\) of the resulting pieces in terms of \(v_0\). \[ v_1 = \_\_\_\_ \, v_0 \] \[ v_2 = \_\_\_\_ \, v_0 \] **Diagram Details:** - The initial object of mass \(3M\) is represented by a blue sphere moving to the right with velocity \(v_0\). - After the break, there are two smaller spheres: - The green sphere has a mass of \(2M\) and is moving at an unknown velocity \(v_2\) at an angle \(\theta_2 = 20.0^\circ\). - The orange sphere has a mass of \(M\) and is moving at an unknown velocity \(v_1\) at an angle \(\theta_1 = 64.0^\circ\).
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