Rain falling vertically will make vertical streaks on a car's side window. however, if the car is moving, the streaks are slanted. if the streaks feom na vertically falling rain make 45 degree angle streaks, how fast is the car moving compared with the apeed of the falling rain?

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