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
lagrange-multiplier
asked Nov 19 at 14:53
dra42841
11
add a comment |
up vote
0
down vote
favorite
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
asked Nov 19 at 14:53
dra42841
11
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
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
asked Nov 19 at 14:53
dra42841
11
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
asked Nov 19 at 14:53
dra42841
11
asked Nov 19 at 14:53
dra42841
11
asked Nov 19 at 14:53
dra42841
11
asked Nov 19 at 14:53
dra42841
11
asked Nov 19 at 14:53
dra42841
11
11
add a comment |
add a comment |
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