**Projectile Motion and Inclined Plane**

To solve this problem, we need to analyze the projectile motion of the ball as it is projected horizontally from the top of the inclined plane. Let's break down the problem into smaller steps:

**Step 1: Analyzing the Motion**
- The ball is projected horizontally, which means its initial velocity in the vertical direction is zero.
- The only force acting on the ball is the force of gravity, which acts vertically downward.
- The ball will experience motion in the horizontal and vertical directions simultaneously.

**Step 2: Resolving the Forces**
- Resolve the gravitational force acting on the ball into two components: one parallel to the inclined plane (mg sinθ) and one perpendicular to the inclined plane (mg cosθ), where θ is the angle of inclination (45 degrees in this case).

**Step 3: Motion in the Vertical Direction**
- Since the initial vertical velocity is zero, the motion in the vertical direction will be influenced by gravity alone.
- The time taken by the ball to reach the inclined plane can be determined using the equation: h = (1/2)gt^2, where h is the height of the plane and g is the acceleration due to gravity.

**Step 4: Motion in the Horizontal Direction**
- The horizontal motion of the ball remains unaffected by gravity.
- The horizontal distance covered by the ball can be calculated using the equation: d = v * t, where v is the horizontal velocity of the ball and t is the time taken to reach the inclined plane.

**Step 5: Calculating the Horizontal Velocity**
- The horizontal velocity of the ball remains constant throughout its motion.
- The horizontal velocity (v) can be determined using the equation: v = √(2g * h), where g is the acceleration due to gravity and h is the height of the plane.

**Step 6: Calculating the Horizontal Distance**
- Substituting the value of v and t in the equation d = v * t, we can calculate the horizontal distance covered by the ball.

**Final Answer**
The ball will strike the inclined plane at a horizontal distance, which can be calculated using the above steps and equations. Remember to plug in the appropriate values for the given speed (v) and angle of inclination (45 degrees).

√x�+h� =√2(2v�/g)� =√2 (2v�/g)