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find a formula to cacluate if a moving object goes to a target
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I am struggling to find a formula to calculate if a moving object goes towards a certain direction. I have $P_1$, which is the current position $(x_1, y_1)$, and its direction angle. I also have the position of a target $(x_2, y_2)$. How can I calculate if the currently moving object goes toward the target position?
mathematical-physics
edited Jan 31 at 15:36
jvdhooft
5,65961641
asked Jan 31 at 15:21
AodyAody
1
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add a comment |
$begingroup$
I am struggling to find a formula to calculate if a moving object goes towards a certain direction. I have $P_1$, which is the current position $(x_1, y_1)$, and its direction angle. I also have the position of a target $(x_2, y_2)$. How can I calculate if the currently moving object goes toward the target position?
mathematical-physics
edited Jan 31 at 15:36
jvdhooft
5,65961641
asked Jan 31 at 15:21
AodyAody
1
$endgroup$
add a comment |
$begingroup$
I am struggling to find a formula to calculate if a moving object goes towards a certain direction. I have $P_1$, which is the current position $(x_1, y_1)$, and its direction angle. I also have the position of a target $(x_2, y_2)$. How can I calculate if the currently moving object goes toward the target position?
mathematical-physics
edited Jan 31 at 15:36
jvdhooft
5,65961641
asked Jan 31 at 15:21
AodyAody
1
$endgroup$
I am struggling to find a formula to calculate if a moving object goes towards a certain direction. I have $P_1$, which is the current position $(x_1, y_1)$, and its direction angle. I also have the position of a target $(x_2, y_2)$. How can I calculate if the currently moving object goes toward the target position?
mathematical-physics
mathematical-physics
edited Jan 31 at 15:36
jvdhooft
5,65961641
asked Jan 31 at 15:21
AodyAody
1
edited Jan 31 at 15:36
jvdhooft
5,65961641
asked Jan 31 at 15:21
AodyAody
1
edited Jan 31 at 15:36
jvdhooft
5,65961641
edited Jan 31 at 15:36
jvdhooft
5,65961641
edited Jan 31 at 15:36
jvdhooft
5,65961641
5,65961641
asked Jan 31 at 15:21
AodyAody
1
asked Jan 31 at 15:21
AodyAody
1
asked Jan 31 at 15:21
AodyAody
1
1
add a comment |
add a comment |
1 Answer
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More information is necessary to answer this question. If object is moving in a vacuum with no external forces pressing on it, then it will simply keep moving in a straight line in the direction given by the direction angle (which I will call $theta$).
It will hit the target if the vector (x2,y2)-(x1,y1) is proportional (by a positive constant!) to the vector $(cos(theta),sin(theta)).$
If the object is subject to gravity, drag, etc... then the problem becomes more complicated and we need more information (if nothing else we would need the initial velocity of the object). One could solve the problem:
Given initial object (x1,y1) subject only to gravity, target position (x2,y2), the mass of the moving object and the direction angle, how much force is necessary to hit (x2,y2) although this places constraints on the possible initial angle (e.g. we could not shoot the object downward or backward and have it hit the target).
answered Jan 31 at 15:36
marlowmarlow
254
$endgroup$
$begingroup$
Thanks for answering. The moving object is a car. How can I know if vector (x2,y2)-(x1,y1) is proportional to the vector (cos(θ),sin(θ)).
$endgroup$
– Aody
Jan 31 at 16:45
$begingroup$
Calculate both vectors (find actual numbers and plot them in standard position). If you don't see it at that point, I would recommend consulting your textbook for an example! The whole point of this problem as stated is to check if you understand what all of these vector operations (addition, subtraction, angles, etc...) mean. See: en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction and look at the pictures
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– marlow
Jan 31 at 17:20
add a comment |
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1 Answer
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1 Answer
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active
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active
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votes
$begingroup$
More information is necessary to answer this question. If object is moving in a vacuum with no external forces pressing on it, then it will simply keep moving in a straight line in the direction given by the direction angle (which I will call $theta$).
It will hit the target if the vector (x2,y2)-(x1,y1) is proportional (by a positive constant!) to the vector $(cos(theta),sin(theta)).$
If the object is subject to gravity, drag, etc... then the problem becomes more complicated and we need more information (if nothing else we would need the initial velocity of the object). One could solve the problem:
Given initial object (x1,y1) subject only to gravity, target position (x2,y2), the mass of the moving object and the direction angle, how much force is necessary to hit (x2,y2) although this places constraints on the possible initial angle (e.g. we could not shoot the object downward or backward and have it hit the target).
answered Jan 31 at 15:36
marlowmarlow
254
$endgroup$
$begingroup$
Thanks for answering. The moving object is a car. How can I know if vector (x2,y2)-(x1,y1) is proportional to the vector (cos(θ),sin(θ)).
$endgroup$
– Aody
Jan 31 at 16:45
$begingroup$
Calculate both vectors (find actual numbers and plot them in standard position). If you don't see it at that point, I would recommend consulting your textbook for an example! The whole point of this problem as stated is to check if you understand what all of these vector operations (addition, subtraction, angles, etc...) mean. See: en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction and look at the pictures
$endgroup$
– marlow
Jan 31 at 17:20
add a comment |
$begingroup$
More information is necessary to answer this question. If object is moving in a vacuum with no external forces pressing on it, then it will simply keep moving in a straight line in the direction given by the direction angle (which I will call $theta$).
It will hit the target if the vector (x2,y2)-(x1,y1) is proportional (by a positive constant!) to the vector $(cos(theta),sin(theta)).$
If the object is subject to gravity, drag, etc... then the problem becomes more complicated and we need more information (if nothing else we would need the initial velocity of the object). One could solve the problem:
Given initial object (x1,y1) subject only to gravity, target position (x2,y2), the mass of the moving object and the direction angle, how much force is necessary to hit (x2,y2) although this places constraints on the possible initial angle (e.g. we could not shoot the object downward or backward and have it hit the target).
answered Jan 31 at 15:36
marlowmarlow
254
$endgroup$
$begingroup$
Thanks for answering. The moving object is a car. How can I know if vector (x2,y2)-(x1,y1) is proportional to the vector (cos(θ),sin(θ)).
$endgroup$
– Aody
Jan 31 at 16:45
$begingroup$
Calculate both vectors (find actual numbers and plot them in standard position). If you don't see it at that point, I would recommend consulting your textbook for an example! The whole point of this problem as stated is to check if you understand what all of these vector operations (addition, subtraction, angles, etc...) mean. See: en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction and look at the pictures
$endgroup$
– marlow
Jan 31 at 17:20
add a comment |
$begingroup$
More information is necessary to answer this question. If object is moving in a vacuum with no external forces pressing on it, then it will simply keep moving in a straight line in the direction given by the direction angle (which I will call $theta$).
It will hit the target if the vector (x2,y2)-(x1,y1) is proportional (by a positive constant!) to the vector $(cos(theta),sin(theta)).$
If the object is subject to gravity, drag, etc... then the problem becomes more complicated and we need more information (if nothing else we would need the initial velocity of the object). One could solve the problem:
Given initial object (x1,y1) subject only to gravity, target position (x2,y2), the mass of the moving object and the direction angle, how much force is necessary to hit (x2,y2) although this places constraints on the possible initial angle (e.g. we could not shoot the object downward or backward and have it hit the target).
answered Jan 31 at 15:36
marlowmarlow
254
$endgroup$
More information is necessary to answer this question. If object is moving in a vacuum with no external forces pressing on it, then it will simply keep moving in a straight line in the direction given by the direction angle (which I will call $theta$).
It will hit the target if the vector (x2,y2)-(x1,y1) is proportional (by a positive constant!) to the vector $(cos(theta),sin(theta)).$
If the object is subject to gravity, drag, etc... then the problem becomes more complicated and we need more information (if nothing else we would need the initial velocity of the object). One could solve the problem:
Given initial object (x1,y1) subject only to gravity, target position (x2,y2), the mass of the moving object and the direction angle, how much force is necessary to hit (x2,y2) although this places constraints on the possible initial angle (e.g. we could not shoot the object downward or backward and have it hit the target).
answered Jan 31 at 15:36
marlowmarlow
254
answered Jan 31 at 15:36
marlowmarlow
254
answered Jan 31 at 15:36
marlowmarlow
254
answered Jan 31 at 15:36
marlowmarlow
254
254
$begingroup$
Thanks for answering. The moving object is a car. How can I know if vector (x2,y2)-(x1,y1) is proportional to the vector (cos(θ),sin(θ)).
$endgroup$
– Aody
Jan 31 at 16:45
$begingroup$
Calculate both vectors (find actual numbers and plot them in standard position). If you don't see it at that point, I would recommend consulting your textbook for an example! The whole point of this problem as stated is to check if you understand what all of these vector operations (addition, subtraction, angles, etc...) mean. See: en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction and look at the pictures
$endgroup$
– marlow
Jan 31 at 17:20
add a comment |
$begingroup$
Thanks for answering. The moving object is a car. How can I know if vector (x2,y2)-(x1,y1) is proportional to the vector (cos(θ),sin(θ)).
$endgroup$
– Aody
Jan 31 at 16:45
$begingroup$
Calculate both vectors (find actual numbers and plot them in standard position). If you don't see it at that point, I would recommend consulting your textbook for an example! The whole point of this problem as stated is to check if you understand what all of these vector operations (addition, subtraction, angles, etc...) mean. See: en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction and look at the pictures
$endgroup$
– marlow
Jan 31 at 17:20
$begingroup$
Thanks for answering. The moving object is a car. How can I know if vector (x2,y2)-(x1,y1) is proportional to the vector (cos(θ),sin(θ)).
$endgroup$
– Aody
Jan 31 at 16:45
$begingroup$
Thanks for answering. The moving object is a car. How can I know if vector (x2,y2)-(x1,y1) is proportional to the vector (cos(θ),sin(θ)).
$endgroup$
– Aody
Jan 31 at 16:45
$begingroup$
Calculate both vectors (find actual numbers and plot them in standard position). If you don't see it at that point, I would recommend consulting your textbook for an example! The whole point of this problem as stated is to check if you understand what all of these vector operations (addition, subtraction, angles, etc...) mean. See: en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction and look at the pictures
$endgroup$
– marlow
Jan 31 at 17:20
$begingroup$
Calculate both vectors (find actual numbers and plot them in standard position). If you don't see it at that point, I would recommend consulting your textbook for an example! The whole point of this problem as stated is to check if you understand what all of these vector operations (addition, subtraction, angles, etc...) mean. See: en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction and look at the pictures
$endgroup$
– marlow
Jan 31 at 17:20
add a comment |
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