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Two points A and B on the opposite banks of a river line AB the distance is between points A and B is 280 M the velocity of the river current v = 60 m/s is constant over the entire with the river the line ab makes an angle Alpha equals to 53 degrees with the direction of the current the angle beta remains the same during the passage from a to b and from B to a the velocity U and angle btered to line ab should the lawns move to cover the distance AB and back in time T = 128 seconds are?
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Two points A and B on the opposite banks of a river line AB the distan...
Problem Statement:
Two points A and B are located on opposite banks of a river. The distance between points A and B is 280 m. The velocity of the river current v = 60 m/s and is constant throughout the width of the river. The line AB makes an angle α = 53 degrees with the direction of the current. The angle β remains the same during the passage from A to B and from B to A. The velocity U and angle β needed to cover the distance AB and return in time T = 128 seconds are to be determined.
Solution:
To determine the required velocity U and angle β, we can break down the motion of the boat into horizontal and vertical components.
Horizontal Component:
The horizontal component of the boat's velocity is responsible for the motion across the river. Let's denote this component as Vh. The velocity of the river current is given as v = 60 m/s. Since the boat's motion is perpendicular to the river current, the horizontal component of the boat's velocity can be written as:
Vh = U * cos(β)
Vertical Component:
The vertical component of the boat's velocity is responsible for the motion along the river. Let's denote this component as Vv. The velocity of the river current is given as v = 60 m/s. Since the boat's motion is parallel to the river current, the vertical component of the boat's velocity can be written as:
Vv = v + U * sin(β)
Time of Travel:
To determine the required velocity U and angle β, we need to consider the time taken to travel from point A to point B and back to point A. The total time of travel is given as T = 128 seconds.
The time taken to travel from point A to point B can be calculated using the horizontal component of the boat's velocity:
t1 = 280 / Vh
The time taken to travel from point B to point A can be calculated using the vertical component of the boat's velocity:
t2 = 280 / Vv
The total time of travel is the sum of t1 and t2:
T = t1 + t2
Equation for Total Time:
Substituting the expressions for Vh and Vv in terms of U and β, we can write the equation for the total time of travel as:
T = (280 / (U * cos(β))) + (280 / (v + U * sin(β)))
Finding U and β:
To solve for U and β, we need to solve the equation T = (280 / (U * cos(β))) + (280 / (v + U * sin(β))) for U and β.
This equation can be solved numerically using numerical methods or through trial and error. By iterating and adjusting the values of U and β, we can find the values that satisfy the equation and give us a total time of travel equal to T = 128 seconds.
Once the values of U and β are determined, the boat can cover the distance AB and return in time T = 128 seconds by maintaining a velocity U and an angle β with respect to the line AB.
Two points A and B are located on opposite banks of a river. The distance between points A and B is 280 m. The velocity of the river current v = 60 m/s and is constant throughout the width of the river. The line AB makes an angle α = 53 degrees with the direction of the current. The angle β remains the same during the passage from A to B and from B to A. The velocity U and angle β needed to cover the distance AB and return in time T = 128 seconds are to be determined.
Solution:
To determine the required velocity U and angle β, we can break down the motion of the boat into horizontal and vertical components.
Horizontal Component:
The horizontal component of the boat's velocity is responsible for the motion across the river. Let's denote this component as Vh. The velocity of the river current is given as v = 60 m/s. Since the boat's motion is perpendicular to the river current, the horizontal component of the boat's velocity can be written as:
Vh = U * cos(β)
Vertical Component:
The vertical component of the boat's velocity is responsible for the motion along the river. Let's denote this component as Vv. The velocity of the river current is given as v = 60 m/s. Since the boat's motion is parallel to the river current, the vertical component of the boat's velocity can be written as:
Vv = v + U * sin(β)
Time of Travel:
To determine the required velocity U and angle β, we need to consider the time taken to travel from point A to point B and back to point A. The total time of travel is given as T = 128 seconds.
The time taken to travel from point A to point B can be calculated using the horizontal component of the boat's velocity:
t1 = 280 / Vh
The time taken to travel from point B to point A can be calculated using the vertical component of the boat's velocity:
t2 = 280 / Vv
The total time of travel is the sum of t1 and t2:
T = t1 + t2
Equation for Total Time:
Substituting the expressions for Vh and Vv in terms of U and β, we can write the equation for the total time of travel as:
T = (280 / (U * cos(β))) + (280 / (v + U * sin(β)))
Finding U and β:
To solve for U and β, we need to solve the equation T = (280 / (U * cos(β))) + (280 / (v + U * sin(β))) for U and β.
This equation can be solved numerically using numerical methods or through trial and error. By iterating and adjusting the values of U and β, we can find the values that satisfy the equation and give us a total time of travel equal to T = 128 seconds.
Once the values of U and β are determined, the boat can cover the distance AB and return in time T = 128 seconds by maintaining a velocity U and an angle β with respect to the line AB.
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Two points A and B on the opposite banks of a river line AB the distance is between points A and B is 280 M the velocity of the river current v = 60 m/s is constant over the entire with the river the line ab makes an angle Alpha equals to 53 degrees with the direction of the current the angle beta remains the same during the passage from a to b and from B to a the velocity U and angle btered to line ab should the lawns move to cover the distance AB and back in time T = 128 seconds are?
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Two points A and B on the opposite banks of a river line AB the distance is between points A and B is 280 M the velocity of the river current v = 60 m/s is constant over the entire with the river the line ab makes an angle Alpha equals to 53 degrees with the direction of the current the angle beta remains the same during the passage from a to b and from B to a the velocity U and angle btered to line ab should the lawns move to cover the distance AB and back in time T = 128 seconds are? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Two points A and B on the opposite banks of a river line AB the distance is between points A and B is 280 M the velocity of the river current v = 60 m/s is constant over the entire with the river the line ab makes an angle Alpha equals to 53 degrees with the direction of the current the angle beta remains the same during the passage from a to b and from B to a the velocity U and angle btered to line ab should the lawns move to cover the distance AB and back in time T = 128 seconds are? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two points A and B on the opposite banks of a river line AB the distance is between points A and B is 280 M the velocity of the river current v = 60 m/s is constant over the entire with the river the line ab makes an angle Alpha equals to 53 degrees with the direction of the current the angle beta remains the same during the passage from a to b and from B to a the velocity U and angle btered to line ab should the lawns move to cover the distance AB and back in time T = 128 seconds are?.
Two points A and B on the opposite banks of a river line AB the distance is between points A and B is 280 M the velocity of the river current v = 60 m/s is constant over the entire with the river the line ab makes an angle Alpha equals to 53 degrees with the direction of the current the angle beta remains the same during the passage from a to b and from B to a the velocity U and angle btered to line ab should the lawns move to cover the distance AB and back in time T = 128 seconds are? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Two points A and B on the opposite banks of a river line AB the distance is between points A and B is 280 M the velocity of the river current v = 60 m/s is constant over the entire with the river the line ab makes an angle Alpha equals to 53 degrees with the direction of the current the angle beta remains the same during the passage from a to b and from B to a the velocity U and angle btered to line ab should the lawns move to cover the distance AB and back in time T = 128 seconds are? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two points A and B on the opposite banks of a river line AB the distance is between points A and B is 280 M the velocity of the river current v = 60 m/s is constant over the entire with the river the line ab makes an angle Alpha equals to 53 degrees with the direction of the current the angle beta remains the same during the passage from a to b and from B to a the velocity U and angle btered to line ab should the lawns move to cover the distance AB and back in time T = 128 seconds are?.
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