Consider an oblique elastic collision between a moving ball and a stationary ball of the same mass. Both the balls move with the same speed after the collision. After the collision, the angle between the directions of motion of two balls is x degree. Find the value of x.

Explanation

To solve the problem of finding the angle \( x \) between the directions of motion of two balls after an oblique elastic collision, we can follow these steps:

### Step 1: Understand the Collision
In an elastic collision between two balls of the same mass, the velocities of the balls change according to the conservation of momentum and kinetic energy. Since one ball is stationary and the other is moving, we can denote the moving ball's initial velocity as \( \mathbf{V} \) and the stationary ball's initial velocity as \( \mathbf{0} \).

### Step 2: Analyze the Components of Velocity
During the collision, the component of the velocity along the line of impact will be exchanged between the two balls. If we denote the angle of incidence as \( \theta \), the component of the moving ball's velocity along the line of impact is \( V \cos \theta \), and the perpendicular component is \( V \sin \theta \).

### Step 3: Apply Conservation of Momentum
After the collision, both balls move with the same speed \( V' \). The ball that was initially moving transfers its velocity along the line of impact to the stationary ball. Therefore, the stationary ball will acquire a velocity \( V \cos \theta \), while the first ball will retain its perpendicular component \( V \sin \theta \).

### Step 4: Determine the Angle Between the Velocities
After the collision, the two balls move at an angle \( x \) to each other. The first ball moves at an angle \( \theta \) from the original direction, and the second ball moves in the direction of the line of impact. Since the two components of velocity are perpendicular to each other, we can conclude that the angle \( x \) between the two balls' velocities is \( 90^\circ \).

### Final Answer
Thus, the angle \( x \) between the directions of motion of the two balls after the collision is:
\[ x = 90^\circ \]