Q3) Two point like objects with the mass m1 =1 kg and m2= 2.05 kg initially move in the x- direction towards each other with initial speeds vi= 3.91 m/s and v2= 4.21 m/s. After the collision the final velocity vector ui of the point mass mi makes an angle 01 with the initial velocity vector vi and the final velocity vector uz of the point mass m2 makes an angle 02 with the initial velocity vector v2". Both angles are measured when the vectors are tail to tail (see figure) and take values between 0 and 90 degrees.
Q3) Two point like objects with the mass m1 =1 kg and m2= 2.05 kg initially move in the x- direction towards each other with initial speeds vi= 3.91 m/s and v2= 4.21 m/s. After the collision the final velocity vector ui of the point mass mi makes an angle 01 with the initial velocity vector vi and the final velocity vector uz of the point mass m2 makes an angle 02 with the initial velocity vector v2". Both angles are measured when the vectors are tail to tail (see figure) and take values between 0 and 90 degrees.
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Transcribed Image Text:### Collision of Two Point-Like Objects
**Problem Statement:**
Two point-like objects with masses \( m_1 = 1 \, \text{kg} \) and \( m_2 = 2.05 \, \text{kg} \) initially move towards each other in the x-direction with initial speeds \( v_1 = 3.91 \, \text{m/s} \) and \( v_2 = 4.21 \, \text{m/s} \). After the collision, the following changes occur:
- The final velocity vector \( \vec{u}_1 \) of mass \( m_1 \) makes an angle \( \theta_1 \) with the initial velocity vector \( \vec{v}_1 \) of mass \( m_1 \).
- The final velocity vector \( \vec{u}_2 \) of mass \( m_2 \) makes an angle \( \theta_2 \) with the initial velocity vector \( \vec{v}_2 \) of mass \( m_2 \).
Both angles, \( \theta_1 \) and \( \theta_2 \), are measured tail to tail and range between 0 and 90 degrees.
**Diagram Explanation:**
1. **Initial Setup:**
- \( m_1 \) is moving in the positive x-direction with velocity \( \vec{v}_1 \).
- \( m_2 \) is moving in the negative x-direction with velocity \( \vec{v}_2 \).
2. **After Collision:**
- The final velocity \( \vec{u}_1 \) of mass \( m_1 \) makes an angle \( \theta_1 \) with the initial velocity \( \vec{v}_1 \) and lies in the positive x-y plane.
- The final velocity \( \vec{u}_2 \) of mass \( m_2 \) makes an angle \( \theta_2 \) with the initial velocity \( \vec{v}_2 \) and lies in the negative x-y plane.
**Questions:**
a) Given the final speed of mass \( m_1 \) is \( |\vec{u}_1| = 1.42 \, \text{m/s} \) and the angle \( \theta_1 = 21.7^\circ \), find the angle \( \theta
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