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Four persons A,B,C and D are intially at the corners of a square of side length 'd'. If person starts moving with same speed'v' such that each one faces the other always, the persons will meet after time, a)d/v b) √2d/v c)d/2v d)d/√2v Plz explain the answer?
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Four persons A,B,C and D are intially at the corners of a square of si...
Solution:
Given, four persons A, B, C, and D are initially at the corners of a square of side length 'd'. They start moving with the same speed 'v' such that each one faces the other always.
Step 1: Calculate the distance between two persons
Let 'O' be the center of the square. Then, the distance between A and B is given by:
AB = √(OA² + OB²)
= √(d²/2 + d²/2)
= d√2/2
Similarly, the distance between B and C, C and D, and D and A is also d√2/2.
Step 2: Calculate the relative velocity of two persons
Let's take two persons, A and B. They are moving towards each other with a relative velocity of 2v (as each one moves with velocity v and they are moving towards each other).
Step 3: Calculate the time taken by two persons to meet
Let t be the time taken by A and B to meet. Then, the distance travelled by A in time t is vt and the distance travelled by B in time t is also vt. Therefore, the total distance travelled by A and B together in time t is d√2.
Hence, we can write:
d√2 = 2vt
t = d√2/2v
Step 4: Calculate the time taken by all four persons to meet
Since A and B meet in time d√2/2v, the time taken by C and D to meet each other is also d√2/2v. Therefore, all four persons will meet at the center O of the square after a time of:
t = 2(d√2/2v) = d/√2v
Hence, the correct option is (d/√2v).
Given, four persons A, B, C, and D are initially at the corners of a square of side length 'd'. They start moving with the same speed 'v' such that each one faces the other always.
Step 1: Calculate the distance between two persons
Let 'O' be the center of the square. Then, the distance between A and B is given by:
AB = √(OA² + OB²)
= √(d²/2 + d²/2)
= d√2/2
Similarly, the distance between B and C, C and D, and D and A is also d√2/2.
Step 2: Calculate the relative velocity of two persons
Let's take two persons, A and B. They are moving towards each other with a relative velocity of 2v (as each one moves with velocity v and they are moving towards each other).
Step 3: Calculate the time taken by two persons to meet
Let t be the time taken by A and B to meet. Then, the distance travelled by A in time t is vt and the distance travelled by B in time t is also vt. Therefore, the total distance travelled by A and B together in time t is d√2.
Hence, we can write:
d√2 = 2vt
t = d√2/2v
Step 4: Calculate the time taken by all four persons to meet
Since A and B meet in time d√2/2v, the time taken by C and D to meet each other is also d√2/2v. Therefore, all four persons will meet at the center O of the square after a time of:
t = 2(d√2/2v) = d/√2v
Hence, the correct option is (d/√2v).
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Four persons A,B,C and D are intially at the corners of a square of side length 'd'. If person starts moving with same speed'v' such that each one faces the other always, the persons will meet after time, a)d/v b) √2d/v c)d/2v d)d/√2v Plz explain the answer?
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Four persons A,B,C and D are intially at the corners of a square of side length 'd'. If person starts moving with same speed'v' such that each one faces the other always, the persons will meet after time, a)d/v b) √2d/v c)d/2v d)d/√2v Plz explain the answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Four persons A,B,C and D are intially at the corners of a square of side length 'd'. If person starts moving with same speed'v' such that each one faces the other always, the persons will meet after time, a)d/v b) √2d/v c)d/2v d)d/√2v Plz explain the answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four persons A,B,C and D are intially at the corners of a square of side length 'd'. If person starts moving with same speed'v' such that each one faces the other always, the persons will meet after time, a)d/v b) √2d/v c)d/2v d)d/√2v Plz explain the answer?.
Four persons A,B,C and D are intially at the corners of a square of side length 'd'. If person starts moving with same speed'v' such that each one faces the other always, the persons will meet after time, a)d/v b) √2d/v c)d/2v d)d/√2v Plz explain the answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Four persons A,B,C and D are intially at the corners of a square of side length 'd'. If person starts moving with same speed'v' such that each one faces the other always, the persons will meet after time, a)d/v b) √2d/v c)d/2v d)d/√2v Plz explain the answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four persons A,B,C and D are intially at the corners of a square of side length 'd'. If person starts moving with same speed'v' such that each one faces the other always, the persons will meet after time, a)d/v b) √2d/v c)d/2v d)d/√2v Plz explain the answer?.
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