Alright, let's say you want to get from one point to another, in a 3D box. all points have an x, y and z coordinate. Point A has coordinates (25,30,5) while Point B has coordinates (50,26,18). The only given variable other than the coordinates is the speed you are traveling. What is an equation I can use to first find the distance between the two points, and then the time it would take to travel between the two at a fixed speed?
the formula for distance in 3D follows the same pattern as the distance in 2D
Dist = √((delta x)^2 + (delta y)^2 + (delta z)^2)
so Dist = √(25^2 + (-4)^2 + 13^2)
= √810
Time = Distance/Rate would still apply for the time.
To find the distance between two points in a 3D space, you can use the distance formula, which is an extension of the Pythagorean theorem. Here's the formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
In this case, let's use Point A as (x1, y1, z1) with coordinates (25, 30, 5), and Point B as (x2, y2, z2) with coordinates (50, 26, 18). Plugging these values into the formula, we have:
Distance = √((50 - 25)^2 + (26 - 30)^2 + (18 - 5)^2)
This simplifies to:
Distance = √(25^2 + (-4)^2 + 13^2)
Now, let's move on to calculating the time it would take to travel between the two points at a fixed speed. To do this, you need to know the speed at which you are traveling. Let's denote it as "v" for velocity.
Time = Distance / Speed
However, since you only mentioned a fixed speed without specifying the units, we'll just use "v" as the speed for now. Plugging the calculated distance into the formula, we get:
Time = Distance / Speed
Time = √(25^2 + (-4)^2 + 13^2) / v
This equation gives you the time it would take to travel between the two points at the given speed.