To determine the displacement of the queen from the point of rebounding on a carrom board, we first need to visualize the situation. Imagine the carrom board as a square with the queen placed at the center. When the striker hits the queen, it travels towards the front edge, bounces off, and then heads towards the opposite end of the board. Let's break this down step by step.
Understanding the Setup
The carrom board is a square, and for simplicity, let's assume each side of the board is of length 'L'. The center of the board, where the queen is placed, is at the coordinates (L/2, L/2). When the queen is struck, it moves towards one of the edges, say the top edge, and then rebounds off it.
Analyzing the Rebound
When the queen hits the edge of the board, it reflects according to the law of reflection, which states that the angle of incidence is equal to the angle of reflection. If we assume the queen travels straight up towards the top edge, it will rebound back down towards the opposite end of the board.
Calculating the Displacement
The displacement we are interested in is the straight-line distance from the point where the queen rebounds to its final position at the opposite end of the board.
- Let’s denote the rebound point as (x, L) where x is the horizontal position of the queen at the moment of rebounding.
- After rebounding, the queen will move straight down to the bottom edge of the board, which is at y = 0.
The final position of the queen after rebounding will be (x, 0). The displacement can be calculated using the distance formula, which is:
Distance Formula
The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
d = √((x2 - x1)² + (y2 - y1)²)
In our case, the initial point of rebounding is (x, L) and the final position is (x, 0). Plugging these coordinates into the formula gives us:
d = √((x - x)² + (0 - L)²) = √(0 + L²) = L
Final Thoughts
Thus, the displacement of the queen from the point of rebounding to its final position at the opposite end of the board is equal to the length of the side of the carrom board, which is 'L'. This means that regardless of where the queen rebounds along the top edge, the vertical distance to the bottom edge remains constant at 'L'. This principle of displacement being independent of the path taken is a fundamental concept in physics.
