A peacock perching on top of a tree of height 12 metres and a snake which is at a distance thrice to that of the peacock from the base of a tree. A snake run to its hole at he base of a tree ,and a peacock flies towards the snakes in a straight line, assume the velocities of snake and peacock are same. At what distance from the base of the tree will the peacock catches the snake? give me hint please.//

To tackle this problem, let's break it down step by step. The scenario involves a peacock perched on a tree and a snake on the ground. The key here is to visualize the positions and the movements of both animals. Here’s a hint to get you started:

Visualizing the Scenario

Imagine the tree as a vertical line, with the peacock at the top and the snake at the base. The height of the tree is 12 meters. The snake is positioned at a distance from the base of the tree that is three times the distance of the peacock's height. So, if the peacock is directly above the base of the tree, the snake is located 36 meters away from the base (3 times 12 meters).

Understanding the Movement

Both the peacock and the snake are moving towards each other at the same speed. The peacock will fly downwards and horizontally towards the snake, while the snake will move directly towards the base of the tree. Since they have the same velocity, the time it takes for both to reach their respective destinations will be the same.

Setting Up the Problem

To find out where the peacock catches the snake, consider the following:

• The peacock starts at a height of 12 meters.
• The snake starts 36 meters away from the base of the tree.
• Both move towards each other at the same speed.

Calculating the Distances

Let’s denote the distance the peacock travels horizontally as x. Since the snake is moving towards the base of the tree, it will cover the distance of 36 meters minus x. The peacock also has to descend from the height of 12 meters while moving horizontally. You can use the Pythagorean theorem to relate these distances.

Using the theorem, the distance the peacock travels can be expressed as:

Distance = √(x² + 12²)

Since both animals travel for the same amount of time and at the same speed, you can set up an equation based on their distances. This will help you find the value of x, which is the horizontal distance from the base of the tree where the peacock catches the snake.

Now, try to set up the equation and solve for x. This will lead you to the solution of where the peacock catches the snake!