Cannot solve Lagrange multiplier for 2 dimensional problem in cartesian coordinates











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My Q is this :
A rod of fixed length (20m) has its base sliding along the X axis and its top slides up the y axis simultaneously. The rod will hit a 5m by 5m box positioned at the origin of the X-Y axes (i.e. Boxes coords are (5,5), (0,0), (5,0), (0,5) ) What is the max height it can reach up the Y axis ?
Note: I have solved this using trigonometry (18.8133m) with a quadratic in Tan A and Cot A (A is angle between rod and Y axis) - BUT I cannot seem to hit on the right constraint equations to solve it using Lagrange multipliers. Is this possible ?
Constraints I thought of are a2 + b2 = 400 and
y = ax/b + b (a=Y intercept, b=X intercept)
are there other constraints to use also ?
Thanks






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    My Q is this :
    A rod of fixed length (20m) has its base sliding along the X axis and its top slides up the y axis simultaneously. The rod will hit a 5m by 5m box positioned at the origin of the X-Y axes (i.e. Boxes coords are (5,5), (0,0), (5,0), (0,5) ) What is the max height it can reach up the Y axis ?
    Note: I have solved this using trigonometry (18.8133m) with a quadratic in Tan A and Cot A (A is angle between rod and Y axis) - BUT I cannot seem to hit on the right constraint equations to solve it using Lagrange multipliers. Is this possible ?
    Constraints I thought of are a2 + b2 = 400 and
    y = ax/b + b (a=Y intercept, b=X intercept)
    are there other constraints to use also ?
    Thanks






    lagrange-multiplier







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    dra42841 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      up vote
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      My Q is this :
      A rod of fixed length (20m) has its base sliding along the X axis and its top slides up the y axis simultaneously. The rod will hit a 5m by 5m box positioned at the origin of the X-Y axes (i.e. Boxes coords are (5,5), (0,0), (5,0), (0,5) ) What is the max height it can reach up the Y axis ?
      Note: I have solved this using trigonometry (18.8133m) with a quadratic in Tan A and Cot A (A is angle between rod and Y axis) - BUT I cannot seem to hit on the right constraint equations to solve it using Lagrange multipliers. Is this possible ?
      Constraints I thought of are a2 + b2 = 400 and
      y = ax/b + b (a=Y intercept, b=X intercept)
      are there other constraints to use also ?
      Thanks






      lagrange-multiplier







      share|cite|improve this question







      New contributor




      dra42841 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      My Q is this :
      A rod of fixed length (20m) has its base sliding along the X axis and its top slides up the y axis simultaneously. The rod will hit a 5m by 5m box positioned at the origin of the X-Y axes (i.e. Boxes coords are (5,5), (0,0), (5,0), (0,5) ) What is the max height it can reach up the Y axis ?
      Note: I have solved this using trigonometry (18.8133m) with a quadratic in Tan A and Cot A (A is angle between rod and Y axis) - BUT I cannot seem to hit on the right constraint equations to solve it using Lagrange multipliers. Is this possible ?
      Constraints I thought of are a2 + b2 = 400 and
      y = ax/b + b (a=Y intercept, b=X intercept)
      are there other constraints to use also ?
      Thanks






      lagrange-multiplier




      lagrange-multiplier






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