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A peacock is sitting on top of a pillar, which is 9m high . From a point 27m away from bottom of pillar, snake is coming to its hole at base of pillar. Seeing the snake the peacock pounces on it. If their speed are equal, at what distance from the whole is the snake caught?
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Problem:
A peacock is sitting on top of a pillar, which is 9m high. From a point 27m away from the bottom of the pillar, a snake is coming to its hole at the base of the pillar. Seeing the snake, the peacock pounces on it. If their speed is equal, at what distance from the hole is the snake caught?
Solution:
Let's assume the distance from the hole to the point where the peacock catches the snake is x meters.
Step 1: Determine the distance traveled by the snake
The snake has to travel a distance of 27 meters from its hole to the point where the peacock catches it.
Step 2: Determine the distance traveled by the peacock
The peacock has to travel a distance equal to the length of the hypotenuse of a right-angled triangle with sides 9m and (27 - x) m.
Using Pythagoras theorem, we get:
Hypotenuse^2 = Base^2 + Height^2
Hypotenuse^2 = (27 - x)^2 + 9^2
Hypotenuse^2 = 729 - 54x + x^2 + 81
Hypotenuse^2 = x^2 - 54x + 810
Step 3: Equate the distance traveled by the snake and the peacock
As the speeds of the snake and the peacock are equal, we can equate the distance traveled by both of them.
Distance traveled by the snake = Distance traveled by the peacock
27 = x^2 - 54x + 810
x^2 - 54x + 783 = 0
Step 4: Solve for x
Using the quadratic formula, we get:
x = (54 ± √(54^2 - 4*1*783))/2
x = (54 ± √(2916 - 3132))/2
x = (54 ± √216)/2
x = 27 ± 6
Since the distance cannot be negative, we take x = 21.
Therefore, the snake is caught by the peacock at a distance of 21 meters from its hole.
A peacock is sitting on top of a pillar, which is 9m high. From a point 27m away from the bottom of the pillar, a snake is coming to its hole at the base of the pillar. Seeing the snake, the peacock pounces on it. If their speed is equal, at what distance from the hole is the snake caught?
Solution:
Let's assume the distance from the hole to the point where the peacock catches the snake is x meters.
Step 1: Determine the distance traveled by the snake
The snake has to travel a distance of 27 meters from its hole to the point where the peacock catches it.
Step 2: Determine the distance traveled by the peacock
The peacock has to travel a distance equal to the length of the hypotenuse of a right-angled triangle with sides 9m and (27 - x) m.
Using Pythagoras theorem, we get:
Hypotenuse^2 = Base^2 + Height^2
Hypotenuse^2 = (27 - x)^2 + 9^2
Hypotenuse^2 = 729 - 54x + x^2 + 81
Hypotenuse^2 = x^2 - 54x + 810
Step 3: Equate the distance traveled by the snake and the peacock
As the speeds of the snake and the peacock are equal, we can equate the distance traveled by both of them.
Distance traveled by the snake = Distance traveled by the peacock
27 = x^2 - 54x + 810
x^2 - 54x + 783 = 0
Step 4: Solve for x
Using the quadratic formula, we get:
x = (54 ± √(54^2 - 4*1*783))/2
x = (54 ± √(2916 - 3132))/2
x = (54 ± √216)/2
x = 27 ± 6
Since the distance cannot be negative, we take x = 21.
Therefore, the snake is caught by the peacock at a distance of 21 meters from its hole.
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A peacock is sitting on top of a pillar, which is 9m high . From a point 27m away from bottom of pillar, snake is coming to its hole at base of pillar. Seeing the snake the peacock pounces on it. If their speed are equal, at what distance from the whole is the snake caught?
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A peacock is sitting on top of a pillar, which is 9m high . From a point 27m away from bottom of pillar, snake is coming to its hole at base of pillar. Seeing the snake the peacock pounces on it. If their speed are equal, at what distance from the whole is the snake caught? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A peacock is sitting on top of a pillar, which is 9m high . From a point 27m away from bottom of pillar, snake is coming to its hole at base of pillar. Seeing the snake the peacock pounces on it. If their speed are equal, at what distance from the whole is the snake caught? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A peacock is sitting on top of a pillar, which is 9m high . From a point 27m away from bottom of pillar, snake is coming to its hole at base of pillar. Seeing the snake the peacock pounces on it. If their speed are equal, at what distance from the whole is the snake caught?.
A peacock is sitting on top of a pillar, which is 9m high . From a point 27m away from bottom of pillar, snake is coming to its hole at base of pillar. Seeing the snake the peacock pounces on it. If their speed are equal, at what distance from the whole is the snake caught? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A peacock is sitting on top of a pillar, which is 9m high . From a point 27m away from bottom of pillar, snake is coming to its hole at base of pillar. Seeing the snake the peacock pounces on it. If their speed are equal, at what distance from the whole is the snake caught? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A peacock is sitting on top of a pillar, which is 9m high . From a point 27m away from bottom of pillar, snake is coming to its hole at base of pillar. Seeing the snake the peacock pounces on it. If their speed are equal, at what distance from the whole is the snake caught?.
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A peacock is sitting on top of a pillar, which is 9m high . From a point 27m away from bottom of pillar, snake is coming to its hole at base of pillar. Seeing the snake the peacock pounces on it. If their speed are equal, at what distance from the whole is the snake caught?, a detailed solution for A peacock is sitting on top of a pillar, which is 9m high . From a point 27m away from bottom of pillar, snake is coming to its hole at base of pillar. Seeing the snake the peacock pounces on it. If their speed are equal, at what distance from the whole is the snake caught? has been provided alongside types of A peacock is sitting on top of a pillar, which is 9m high . From a point 27m away from bottom of pillar, snake is coming to its hole at base of pillar. Seeing the snake the peacock pounces on it. If their speed are equal, at what distance from the whole is the snake caught? theory, EduRev gives you an
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