3D Velocity Of A Moving Object To A Stationary Object

[phys123]

There are 2 objects. Object 1 is stationary and Object 2 is in motion. Object 1's position in the 3D world is (x=0,y=0,z=0). I have Object 2's velocity (also in x,y,z directions). I need to calculate the speed at which Object 2 is moving towards (or away from) Object 1. Keep in mind that this will not be Object 2's speed, because it is not moving directly towards Object 1. It is moving on it's own path, but I need to know the change in speed towards Object 1. Hope I explained that good enough, if not then ask. How can this be done?

 

[Doc Al]

You'll need Object 2's position. At any moment, find the component of Object 2's velocity parallel to its position vector with respect to the origin. That will be the rate of change of the distance between the Objects.

 

[phys123]

I do have Object 2's position, forgot to mention that. And what you are saying is exactly what I need to do. Can you go into detail on how I would calculate this? My physics isn't very strong

 

[Doc Al]

Not much physics here, just a bit of math. Find the unit vector pointing from 1 to 2--that gives you the direction. To find the component of 2's velocity in that direction, take the scalar product of the velocity with that unit vector.

 

[PJC01]

To calculate the speed at which Object 2 is moving towards or away from Object 1, we can use the concept of relative velocity. This involves calculating the velocity of Object 2 relative to Object 1.

First, we need to find the vector distance between Object 1 and Object 2 at a specific point in time. This can be done by subtracting the coordinates of Object 1 (0,0,0) from the coordinates of Object 2 (x,y,z). This will give us a vector representing the distance between the two objects in the x,y,z directions.

Next, we can use the formula for relative velocity, which states that the relative velocity of Object 2 with respect to Object 1 is equal to the velocity of Object 2 minus the velocity of Object 1. In this case, we are only interested in the x,y,z components of the velocity, so we can ignore the z component of Object 1's velocity (since it is stationary).

Finally, we can calculate the magnitude of the relative velocity vector using the Pythagorean theorem, which will give us the speed at which Object 2 is moving towards or away from Object 1.

It is important to note that this method will only give us the instantaneous speed at a specific point in time. If we want to calculate the average speed over a longer period of time, we will need to use calculus to integrate the velocity over the desired time interval.

I hope this explanation helps. If you have any further questions, please let me know.