When car is at rest the steaks makes makes vertical lines
which means the rain is falling in vertically downward direction
Now when car is moving with some speed v
Now the steaks makes and an angle 45 degree
So here we can say that relative velocity of rain with car is 45 degree
Now this is the resultant speed of rain in car frame
now if relative velocity makes 45 degree angle so this vector must have same components in vertical and horizontal direction
Since we know that relative velocity is resultant of rain velocity and car velocity so we can say here its two components are rain velocity and car velocity
So these two components must be of same magnitude
as it makes 45 degree
because when two vector are of same magnitude then the resultant vector always makes 45 degree with them if these two vectors are perpendicular to each other
car is moving at same speed as the speed of rain