Two vehicles are approaching an intersection. One is a 2500-kg pickup traveling at 14.0 m/s from east to west (the -x-direction), and the other is a 1500-kg sedan going from south to north (the +y-direction) at 23.0 m/s. (a) Find the x- and y-components of the net momentum of this system. (b) What are the magnitude and direction of the net momentum?
Solution 4E a) The velocity of the 2500 kg vehicle is 14 m/s. The velocity of the 1500 kg sedan is 23 m/s. But velocity is a vector quantity and there is a direction associated with it. So, let the diagram be as a xy coordinate system. So, The velocity of the 2500 kg vehicle is -14 m/s. The velocity of the 1500 kg sedan is +23 m/s. These are the only components and the other two components are zero. The x component of momentum of the 2500 kg vehicle is, P 1x= 2500kg × ( 14 m/s) = 35000 kg m/s The y component is, P 1y = 0 The x component of the 1500 kg vehicle is, P2x = 0 The y component of the vehicle is, P 2y= 1500kg × 23 m/s = 34500 kg m/s. Net momentum x and y components are, P = 35000 & P = 34500. x y b) he net momentum is, 2 2 0 P = P x + P y + 2P x cys 90 2 2 = 5000 + 34500 + 2 × 35000 × 34500 × 1 = 69500 kg m/s. The direction is towards the north-west direction.