Question

A car of mass m1 = 2000.0kg is moving at speed v1i = 20.0m/s towards East. A truck of mass m2 = 5000.0kg is moving at speed v2i = 10.0m/s towards North. They collide at an intersection and get entangled (complete inelastic collision).
1. What is the magnitude and direction of the final velocity of the entangled automobiles?
2. How much kinetic energy is lost in the collision. That is, calculate the change in the kinetic energy of the system

Answer 1

Me = East momentum = 2000*20
Mn = North momentum = 5000*10

that remains the same so after
Me = 7000 Veast = 2000*20 so Ve = 40/7
Mn = 7000 Vnorth = 5000 *10 so Vn = 50/7

|v| = (1/7)sqrt(40^2+50^2)
tan angle east of north = Ve/Vn

Ke before = (1/2)2000*400 + (1/2)5000*100
Ke after = (1/2) 7000 * |v|^2