Consider the collision depicted in Figure, to be between two billiard balls with equal masses `m_(1)=m_(2)`. The first ball is called the cue and the second ball is called the target. The billiard player wants to sink the target ball in a corner pocket, which is at an angle `theta_(2)=phi=37^(@)`. Assume that the collision is elastic and that friction and rotational motion are not important. Obtain `theta_(1)=theta` .

Explanation

To solve the problem of finding the angle \(\theta_1 = \theta\) for the collision between two billiard balls, we will use the principles of conservation of momentum and conservation of kinetic energy, as the collision is elastic. Here are the steps to derive the solution:

### Step-by-Step Solution:

1. **Identify the Variables**:
- Let the mass of both balls be \(m_1 = m_2 = m\).
- The initial velocity of the cue ball (ball 1) is \(u_1 = U\) and it is moving at an angle \(\theta\) with respect to the x-axis.
- The target ball (ball 2) is initially at rest, so its initial velocity \(u_2 = 0\).
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