Sample Problems

Vector addition and subtraction is essential to anyone who wants to learn directions, positions, etc. It is useful in navigation and in solving problems which involve knowning the quickest way to go places. It is also useful in fields where it is essential to know where things are going.  Vectors can be used when talking about momentum. For example, If Jack is going 12 m/s  [ N 30 degrees E] across a river and the river was flowing at 5 m/s [S 25 degrees W] what is the actual velocity in relationship to the bank of the river. sin 30 = opp/12 m/s     opp= 6m/s [E] cos 30 = adj/12 m/s     adj = 10.41 m/s [N] sin 25 = opp/5 m/s       opp = 2.11 m/s [W] cos 25 = adj/5 m/s        adj = 4.53 m/s [S] 10.41 m/s [N] - 4.53 m/s [S] =  5.88 [N] 6m/s [E] - 2.11 m/s [W] = 3.89 m/s [E] tanx=3.89 m/s [E] / 5.88 m/s [N]    x=33.49 degrees hyp= 3.89 m/s [E] / sin 33.49 degrees hyp = 7.05 m/s [N 33.49 degrees E] Jack will be moving at 7.05 m/s  [N 33.49 degrees E] Kinematics problems are useful when you need to calculate the distance an object is going to go or just to find out an accerlation or decceleration.  It is especially useful when you want to calculate these things due to gravity.  In real life these would be used to find the location of falling objects which are moving horizontally and vertically.   For example, A parachutist is in a plane moving 10 m/s [W].  The parachutist jumps out of the moving plane and decends to the ground below without opening his parachute. The parachutist falls for 9 seconds.   At what velocity does the parachutist hit and where in relation to the plane does it hit. 0 m/s = Vf + (9.8 m/s2)(9s) The parachutist lands at 88.2 m/s and it is directly below the plane.