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Two swimmers leave point A to point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B. What was the velocity u of his walking if both swimmers reached the destination simultaneously? The stream velocity v0 = 2.0 km/hour and the velocity if of each swimmer with respect to water equals 2.5 km per hour.?
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Two swimmers leave point A to point B lying right across on the other ...
**Solution:**
To solve this problem, let's consider the motion of each swimmer separately and then analyze the conditions for them to reach the destination simultaneously.
Let's assume that the distance between point A and point B is D.
**Swimmer Crossing the River Along the Straight Line AB:**
The first swimmer swims directly across the river from point A to point B. The velocity of this swimmer with respect to the water is given as 2.5 km/hour.
**Swimmer Swimming at Right Angles to the Stream:**
The second swimmer swims at right angles to the stream and is carried away by the stream. The velocity of this swimmer with respect to the water is also given as 2.5 km/hour. However, due to the stream's velocity, the swimmer is carried downstream.
The stream's velocity is given as 2.0 km/hour. So, the effective velocity of the second swimmer with respect to the ground (or the velocity at which the swimmer is carried away by the stream) is:
v_effective = v_swimmer + v_stream
= 2.5 km/hour + 2.0 km/hour
= 4.5 km/hour
This means that the second swimmer is being carried downstream at a velocity of 4.5 km/hour.
**Walking the Distance Carried Away by the Stream:**
Once the second swimmer reaches the other bank of the river, the swimmer walks the distance that he has been carried away by the stream to reach point B.
Let's assume that the distance the second swimmer is carried away by the stream is x km.
The time taken for the first swimmer to reach point B is given by:
t1 = D / 2.5 (since the velocity of the first swimmer is 2.5 km/hour)
The time taken for the second swimmer to reach point B is given by:
t2 = (D + x) / 4.5 (since the effective velocity of the second swimmer is 4.5 km/hour)
Since both swimmers reach point B simultaneously, the time taken by both swimmers should be the same. Therefore:
t1 = t2
D / 2.5 = (D + x) / 4.5
Solving this equation for x, we can find the distance the second swimmer is carried away by the stream.
Once we have the value of x, we can find the velocity of the second swimmer's walking by dividing the distance x by the time taken by the second swimmer to walk that distance.
Therefore, the velocity u of the second swimmer's walking is:
u = x / ((D + x) / 4.5)
Simplifying this expression, we can calculate the value of u.
Note: The exact numerical calculation of u will depend on the specific values of D, v0, and vi given in the problem.
To solve this problem, let's consider the motion of each swimmer separately and then analyze the conditions for them to reach the destination simultaneously.
Let's assume that the distance between point A and point B is D.
**Swimmer Crossing the River Along the Straight Line AB:**
The first swimmer swims directly across the river from point A to point B. The velocity of this swimmer with respect to the water is given as 2.5 km/hour.
**Swimmer Swimming at Right Angles to the Stream:**
The second swimmer swims at right angles to the stream and is carried away by the stream. The velocity of this swimmer with respect to the water is also given as 2.5 km/hour. However, due to the stream's velocity, the swimmer is carried downstream.
The stream's velocity is given as 2.0 km/hour. So, the effective velocity of the second swimmer with respect to the ground (or the velocity at which the swimmer is carried away by the stream) is:
v_effective = v_swimmer + v_stream
= 2.5 km/hour + 2.0 km/hour
= 4.5 km/hour
This means that the second swimmer is being carried downstream at a velocity of 4.5 km/hour.
**Walking the Distance Carried Away by the Stream:**
Once the second swimmer reaches the other bank of the river, the swimmer walks the distance that he has been carried away by the stream to reach point B.
Let's assume that the distance the second swimmer is carried away by the stream is x km.
The time taken for the first swimmer to reach point B is given by:
t1 = D / 2.5 (since the velocity of the first swimmer is 2.5 km/hour)
The time taken for the second swimmer to reach point B is given by:
t2 = (D + x) / 4.5 (since the effective velocity of the second swimmer is 4.5 km/hour)
Since both swimmers reach point B simultaneously, the time taken by both swimmers should be the same. Therefore:
t1 = t2
D / 2.5 = (D + x) / 4.5
Solving this equation for x, we can find the distance the second swimmer is carried away by the stream.
Once we have the value of x, we can find the velocity of the second swimmer's walking by dividing the distance x by the time taken by the second swimmer to walk that distance.
Therefore, the velocity u of the second swimmer's walking is:
u = x / ((D + x) / 4.5)
Simplifying this expression, we can calculate the value of u.
Note: The exact numerical calculation of u will depend on the specific values of D, v0, and vi given in the problem.
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Two swimmers leave point A to point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B. What was the velocity u of his walking if both swimmers reached the destination simultaneously? The stream velocity v0 = 2.0 km/hour and the velocity if of each swimmer with respect to water equals 2.5 km per hour.?
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Two swimmers leave point A to point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B. What was the velocity u of his walking if both swimmers reached the destination simultaneously? The stream velocity v0 = 2.0 km/hour and the velocity if of each swimmer with respect to water equals 2.5 km per hour.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two swimmers leave point A to point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B. What was the velocity u of his walking if both swimmers reached the destination simultaneously? The stream velocity v0 = 2.0 km/hour and the velocity if of each swimmer with respect to water equals 2.5 km per hour.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two swimmers leave point A to point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B. What was the velocity u of his walking if both swimmers reached the destination simultaneously? The stream velocity v0 = 2.0 km/hour and the velocity if of each swimmer with respect to water equals 2.5 km per hour.?.
Two swimmers leave point A to point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B. What was the velocity u of his walking if both swimmers reached the destination simultaneously? The stream velocity v0 = 2.0 km/hour and the velocity if of each swimmer with respect to water equals 2.5 km per hour.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two swimmers leave point A to point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B. What was the velocity u of his walking if both swimmers reached the destination simultaneously? The stream velocity v0 = 2.0 km/hour and the velocity if of each swimmer with respect to water equals 2.5 km per hour.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two swimmers leave point A to point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B. What was the velocity u of his walking if both swimmers reached the destination simultaneously? The stream velocity v0 = 2.0 km/hour and the velocity if of each swimmer with respect to water equals 2.5 km per hour.?.
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Two swimmers leave point A to point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B. What was the velocity u of his walking if both swimmers reached the destination simultaneously? The stream velocity v0 = 2.0 km/hour and the velocity if of each swimmer with respect to water equals 2.5 km per hour.?, a detailed solution for Two swimmers leave point A to point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B. What was the velocity u of his walking if both swimmers reached the destination simultaneously? The stream velocity v0 = 2.0 km/hour and the velocity if of each swimmer with respect to water equals 2.5 km per hour.? has been provided alongside types of Two swimmers leave point A to point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B. What was the velocity u of his walking if both swimmers reached the destination simultaneously? The stream velocity v0 = 2.0 km/hour and the velocity if of each swimmer with respect to water equals 2.5 km per hour.? theory, EduRev gives you an
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