You walk  km at deg south of east and then walk  km at deg north of east. To return directly to your starting point, how far and in what direction should you walk? 

 

Two trains, traveling towards one another on a straight track are m apart when the engineers on both trains become aware of the impending collision and hit their brakes. The eastbound train, initially moving at kmh slows down at ms The westbound train, initially moving at kmh slows down at ms Will the trains stop before colliding? If so what is the distance between them once they have stopped? If not, what initial separation distance would have been needed to avert a disaster?

A boat is drifting in a strong current that is taking it ms east. To get out of this current, it begins accelerating south at ms After s how far is it from the starting point and what is its velocity? Include both magnitude and direction.

A bicyclist starting at rest accelerates constantly to her top speed of ms over m A What is the acceleration of the bicyclist? B For how much time is the bicyclist accelerating?