**Problem 4: Physics of a Supported Board**A uniform board of length 2.25 meters and mass 34.0 kilograms is supported by three ropes, as illustrated by the blue vectors in the figure. A person weighing 575 Newtons stands a distance \( d \) from the left end of the board. If the tension in rope 3 is given as 465 Newtons, determine the tension in ropes 1 and 2, as well as the distance \( d \).**Figure Explanation:**The diagram shows:- A horizontal board supported by ropes.- Rope 1 (\( T_1 \)) is inclined at an angle of 40.0° to the horizontal.- Rope 2 (\( T_2 \)) is vertical.- Rope 3 (\( T_3 \)) is horizontal and pulls to the left.- The person stands a distance \( d \) from the left end, with a 2.00-meter length from the person to the right end of the board.**Answers:**- Tension in Rope 1 (\( T_1 \)): 607 Newtons- Tension in Rope 2 (\( T_2 \)): 518 Newtons- Distance \( d \): 0.778 metersThis solution exemplifies the equilibrium of forces and the calculation of tensions in a static system involving a plank and person.

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Answered: 4. A uniform board of length 2.25 m and…

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4. A uniform board of length 2.25 m and mass 34.0 kg is supported by three ropes, as indicated by the blue vectors in the figure. A 575-N person stands a distance d to from the left end of the board. If the tension in rope 3 is 465 N, find the tension in ropes 1 and 2 and the distance d.