How, knowing the coordinates of an object in the 2d plane, its angle in directions in radians and speed, calculate new coordinates in a unit of time?

Question

Mathematics

For example:
There is a plane 1000x1000 m., an object is located on it at a point 100x100, the angle of its direction is 0.64 radians, the speed is 1 m / s at what point will the object be in 1 sec?

Answer 1

Путь = время * скорость

1. Find the length it will go.
   
2. There is a length, there is an angle - this is the displacement vector.
   
3. It is necessary to add the vectors of the initial position and displacement.
   

Новый_X = Старый_X + Путь * cos(угла)
Новый_Y = Старый_Y + Путь * sin(угла)

Answer 2

The problem described in your question is dealt with by the section of science trigonometry .
In your case, the change in coordinates along the X and Y axes will be cos(φ) and sin(φ) respectively.
PS This is if the angle φ is measured from the direction of the X axis counterclockwise.