In kinematics for finding of various sizes mathematical methods are used. In particular, to find the movement vector module, it is necessary to apply a formula from vector algebra. Coordinates of points of the beginning and the end of a vector, i.e. the initial and final provision of a body appear in it.
Instruction
1. During the movement the material body changes the position in space. Its trajectory can be a straight line or any, its length is a way of a body, but not distance to which it moved. These two sizes coincide only in case of the rectilinear movement.
2. So, let the body made some movement from a point And (h0, u0) in a point In (x, s). To find the movement vector module, it is necessary to calculate AV vector length. Draw coordinate axes and apply on them the known points of initial and final position of a body And yes Century.
3. Carry out a piece from a point And to a point In, specify the direction. Lower projections of its ends to axes and put the pieces parallel and equal to them passing through the considered points on graphics. You will see that in the drawing the rectangular triangle with legs projections and a hypotenuse movement was designated.
4. On Pythagorean theorem find hypotenuse length. This method is widely applied in vector algebra and carries the name of the rule of a triangle. For a start write down lengths of legs, they are equal to the differences between the corresponding abscissae and ordinates of points And yes In: ABx = x – x0 – a vector projection to an axis Oh; ABy = y – y0 – its projection to Ou's axis.
5. Determine movement |AB|: by |AB| = √ (ABx² + ABy²) = ((x – x0)² + (y – y0)²).
6. For three-dimensional space add to a formula the third coordinate – z z-coordinate: |AB| = √ (ABx² + ABy² + ABz²) = ((x – x0)² + (y – y0)² + (z – z0)²).
7. The received formula can be applied to any trajectory and type of the movement. At the same time the size of movement has important property. It always less or is equal to length of a way, generally its line does not coincide from a curve trajectory. Projections are sizes mathematical, can be as more, and it is less than zero. However it does not matter as in calculation they participate in even degree.