How do I break a moving objects speed up into its X and Y velocity given a fixed speed/angle?

Question

Math escapes me today.

How do I find the X speed and the Y speed of an object if it is going at a defined speed (say, 5 pixels/second) at a 45 degree angle?

Answer 1

At a 45 degree angle, an object is going sqrt(2)/2 of the speed along each axis. Generally, you can do it with sin and cosine, but for specific angles like this you can do it just by knowing pythagorean triangles.

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. You know the hypotenuse is V. You also know that the other two sides equal each other. That means that V^2 = Vx^2 * 2. This means that Vx = sqrt(V^2/2), which equals V * sqrt(1/2).

Answer 2

It will be Vx=VCos@
Vy=Vsin@
So in your case it will be Vx=5*cos45 and Vy=5*sin45
At 45 angle value of Cos & Sin is same i.e 1/root 2.

Note: If you are doing any math stuff in programming then have a look at Vecmath lib.

Answer 3

So always 5 pixels/sec and always 45 degrees?

The general case is

 velx=cos(a)*vel;
 vely=sin(a)*vel;

a is angle, usually in radians, so convert from degrees, and the signs (positive/negative) will depend on your coordinate system.

Crazy fact from the 1980s: In the old days, we used lookup tables for sin and cos!

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Edited: Made my axes more conventional thanks to comment below. x is positive to your right. y is positive up. 45 degrees is to the northeast. If you have something else, let me know.