# Finding distance between two points A, B moving in a plane

• Richlair
In summary, A and B are initially at a distance d apart in a plane. B moves perpendicular to the line AB with speed v, while A moves with the same speed towards B. After some time, both A and B are moving in the same direction and will be a fixed distance apart. The fixed distance can be found by considering the velocities and constraints of both particles.
Richlair
A and B are two objects in a plane. Initially they were at a distance d apart. B moves rectilinearly and perpendicular to the line AB initially with speed v and A moves with speed v so that it is continually aimed towards B. After some time, both of them are moving aimed in the same direction and would be a fixed distance apart. Find the fixed distance.

Richlair said:
A and B are two objects in a plane. Initially they were at a distance d apart. B moves rectilinearly and perpendicular to the line AB initially with speed v and A moves with speed v so that it is continually aimed towards B. After some time, both of them are moving aimed in the same direction and would be a fixed distance apart. Find the fixed distance.
I assume that their speed |velocity| is same
First consider first particle A is at 0i+0j and second particle B is at di+0j here i and j represent unit vectors along x and y direction. now B start moving with velocity Vb=0i+vj it's location at time t is Rb=(0i+vj)t+di. Now come to first particle A. let it's velocity at any time is vx i+vy j. since velocity of both A and B is same so (vx2+vy2))1/2=v. one more constraint is it's direction is always along the location of B that is (0i+vj)t+di now using all the constraint i mentioned you can do this question.
Hope now you will complete it.

vkash said:
I assume that their speed |velocity| is same
First consider first particle A is at 0i+0j and second particle B is at di+0j here i and j represent unit vectors along x and y direction. now B start moving with velocity Vb=0i+vj it's location at time t is Rb=(0i+vj)t+di. Now come to first particle A. let it's velocity at any time is vx i+vy j. since velocity of both A and B is same so (vx2+vy2))1/2=v. one more constraint is it's direction is always along the location of B that is (0i+vj)t+di now using all the constraint i mentioned you can do this question.
Hope now you will complete it.

I was thinking much the same, but I would solve it in B's frame of reference. That mean treating B as at rest and A with initial leftward velocity of v and initial downward velocity (assuming B was moving upwards) of -v.

vkash said:
I assume that their speed |velocity| is same
First consider first particle A is at 0i+0j and second particle B is at di+0j here i and j represent unit vectors along x and y direction. now B start moving with velocity Vb=0i+vj it's location at time t is Rb=(0i+vj)t+di. Now come to first particle A. let it's velocity at any time is vx i+vy j. since velocity of both A and B is same so (vx2+vy2))1/2=v. one more constraint is it's direction is always along the location of B that is (0i+vj)t+di now using all the constraint i mentioned you can do this question.
Hope now you will complete it.

How should I use the constraint that A is headed towards B at any instant?

I would approach this problem by first visualizing the scenario described. A and B are two objects initially at a distance d apart in a plane. B is moving perpendicular to the line AB with a constant speed v, while A is also moving with the same speed v, but continually aimed towards B.

To find the fixed distance between A and B after some time, we can use the concept of relative velocity. Since A is continually aimed towards B, its velocity relative to B is always in the direction of B's motion. This means that we can consider B's motion as the reference frame, and A's motion as the relative motion.

Using the formula for relative velocity, we can calculate the velocity of A relative to B as vAB = vA - vB. Since vA = v and vB = v, we can substitute these values to get vAB = v - v = 0. This means that A and B are moving at the same speed in the same direction relative to each other.

Now, we can use the formula for distance traveled, d = vt, where d is the distance, v is the velocity, and t is the time. Since both A and B are moving at the same speed, we can set their distance traveled to be equal and solve for the time t.

dA = dB
vAt = vBt
t = d/v

Substituting this value of t into the formula for distance, we get the fixed distance between A and B after some time as d = vt = v(d/v) = d. This means that the fixed distance between A and B is the same as their initial distance d.

In conclusion, the fixed distance between A and B after some time is equal to their initial distance d. This can be explained by the fact that both objects are moving at the same speed and in the same direction, maintaining a constant distance between them.

## What is the formula for finding the distance between two points A and B in a plane?

The distance between two points A(x1,y1) and B(x2,y2) can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse (c) of a right triangle is equal to the sum of the squares of the other two sides (a and b). Therefore, the formula for finding the distance between A and B is:

Distance = √((x2-x1)^2 + (y2-y1)^2)

## What units should be used for the coordinates of points A and B when finding the distance between them?

The units for the coordinates of points A and B should be the same, whether they are in inches, feet, meters, or any other unit. It is important to use consistent units to ensure accurate calculations.

## Can the distance between two points A and B be negative?

No, the distance between two points A and B cannot be negative. Distance is a positive quantity and is always represented by a positive value.

## Can the distance between two points A and B be calculated if they are not moving in a straight line?

Yes, the distance between two points A and B can still be calculated even if they are not moving in a straight line. The formula for finding the distance only requires the coordinates of the two points and does not depend on their movement path.

## Is there a difference in calculating the distance between two points A and B in a plane and a three-dimensional space?

Yes, there is a difference in calculating the distance between two points A and B in a plane and a three-dimensional space. In a three-dimensional space, the formula for finding the distance becomes:

Distance = √((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)

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