Two automobiles, each of mass 800kg , are moving at the same speed, 18m/s , when they collide and stick together. At what speed does the wreckage move if one car was driving north and one east.

Answer 1

initial momentum
North 800 * 18
East 800 * 18

final momentum

North 1600 v sin T
East 1600 v cos T

(I am pretending I do not see that V = 18 sqrt 2 and T = 45 degrees)

800 * 18 = 1600 v sin T
800 * 18 = 1600 v cos T
so sin T = cos T = 1/sqrt 2
That is T = 45 degrees
so
800 * 18 = 1600 v /sqrt2
800 * 18 = 800 v /sqrt 2
v = 18 sqrt 2
v = 18 sqrt 2