Consider the east-west direction along x-axis and north-south direction along y-axis. In unit vector notation, velocities can be given as
[tex]\underset{V_{A}}{\rightarrow}[/tex] = velocity of car A before collision = 0 i - [tex]V_{A}[/tex] j
[tex]\underset{V_{B}}{\rightarrow}[/tex] = velocity of car B before collision = [tex]V_{B}[/tex] i + 0 j
[tex]\underset{V_{AB}}{\rightarrow}[/tex] = velocity of combination after collision = (35.8 Cos31.6) i - (35.8 Sin31.6) j = 30.5 i - 18.8 j
[tex]M_{A}[/tex] = mass of car A = 1750 kg
[tex]M_{B}[/tex] = mass of car B = 1450 kg
Using conservation of momentum
[tex]M_{A}[/tex] [tex]\underset{V_{A}}{\rightarrow}[/tex] + [tex]M_{B}[/tex] [tex]\underset{V_{B}}{\rightarrow}[/tex] = ([tex]M_{A}[/tex] + [tex]M_{B}[/tex]) ( [tex]\underset{V_{AB}}{\rightarrow}[/tex] )
(1750) (0 i - [tex]V_{A}[/tex] j) + (1450) ([tex]V_{B}[/tex] i + 0 j) = (1750 + 1450) (30.5 i - 18.8 j)
(1450) [tex]V_{B}[/tex] i - (1750) [tex]V_{A}[/tex] j = 97600 i - 60160 j
Comparing the coefficient of "i" and "j" both side
(1450) [tex]V_{B}[/tex] = 97600 and - (1750) [tex]V_{A}[/tex] = - 60160
[tex]V_{B}[/tex] = 67.3 km/h and [tex]V_{A}[/tex] = 34.4 km/
