A girl riding a bicycle with a speed of 5 m/s towards north direction, observes rain falling vertically down. If she increases her speed to 10 m/s, rain appears to meet her at 45° to the vertical. What is the speed of the rain? In what direction does rain fall as observed by a ground based observer?

(Hint: Assume north to be cap i direction and vertically downward to be - cap **j** . Let the rain velocity** v**_{r} be a cap **i** + b cap **j** . The velocity of rain as observed by the girl is always** v**_{r} -** v**_{rgirl} . Draw the vector diagram/s for the information given and find a and b. You may draw all vectors in the reference frame of ground based observer.)