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Four athletes are standing at the corners A ,B ,C and D of a square of side l . They simultaneously start running, such that A runs towards B ,B runs towards C , C runs towards A, each with velocity v. They will meet at O , after a time .... ..
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Four athletes are standing at the corners A ,B ,C and D of a square o...
**Explanation:**
To solve this problem, we need to consider the relative velocities of the athletes and determine the time it takes for them to meet at point O.
**Relative Velocities:**
Let's consider the velocities of the athletes with respect to each other.
- Athlete A's velocity with respect to B is v.
- Athlete B's velocity with respect to C is v.
- Athlete C's velocity with respect to A is v.
**Velocity Components:**
To simplify the problem, we can break down the velocities into their components along the sides of the square.
- Athlete A's velocity component along AB is v.
- Athlete B's velocity component along BC is v.
- Athlete C's velocity component along CA is v.
**Time to Meet:**
Since the athletes are running towards each other, their relative velocities will add up. To determine the time it takes for them to meet at point O, we need to find the distance they need to cover and divide it by their combined velocity.
- The distance between A and B is l.
- The distance between B and C is l.
- The distance between C and A is l.
Since they are running towards each other, the total distance they need to cover is the sum of these distances, which is 3l.
- The combined velocity of the athletes is 3v, as the relative velocities add up.
- Therefore, the time it takes for them to meet at point O is given by:
Time = Distance / Velocity
= 3l / 3v
= l / v
Hence, the athletes will meet at point O after a time of l/v.
To solve this problem, we need to consider the relative velocities of the athletes and determine the time it takes for them to meet at point O.
**Relative Velocities:**
Let's consider the velocities of the athletes with respect to each other.
- Athlete A's velocity with respect to B is v.
- Athlete B's velocity with respect to C is v.
- Athlete C's velocity with respect to A is v.
**Velocity Components:**
To simplify the problem, we can break down the velocities into their components along the sides of the square.
- Athlete A's velocity component along AB is v.
- Athlete B's velocity component along BC is v.
- Athlete C's velocity component along CA is v.
**Time to Meet:**
Since the athletes are running towards each other, their relative velocities will add up. To determine the time it takes for them to meet at point O, we need to find the distance they need to cover and divide it by their combined velocity.
- The distance between A and B is l.
- The distance between B and C is l.
- The distance between C and A is l.
Since they are running towards each other, the total distance they need to cover is the sum of these distances, which is 3l.
- The combined velocity of the athletes is 3v, as the relative velocities add up.
- Therefore, the time it takes for them to meet at point O is given by:
Time = Distance / Velocity
= 3l / 3v
= l / v
Hence, the athletes will meet at point O after a time of l/v.
Community Answer
Four athletes are standing at the corners A ,B ,C and D of a square o...
l/2v
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Four athletes are standing at the corners A ,B ,C and D of a square of side l . They simultaneously start running, such that A runs towards B ,B runs towards C , C runs towards A, each with velocity v. They will meet at O , after a time .... ..
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Four athletes are standing at the corners A ,B ,C and D of a square of side l . They simultaneously start running, such that A runs towards B ,B runs towards C , C runs towards A, each with velocity v. They will meet at O , after a time .... .. 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 athletes are standing at the corners A ,B ,C and D of a square of side l . They simultaneously start running, such that A runs towards B ,B runs towards C , C runs towards A, each with velocity v. They will meet at O , after a time .... .. covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four athletes are standing at the corners A ,B ,C and D of a square of side l . They simultaneously start running, such that A runs towards B ,B runs towards C , C runs towards A, each with velocity v. They will meet at O , after a time .... ...
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