given that :
UA=15i+30j Ā and UB =-10+5.0j
speed before collision is given as
uā = sqrt(15Ā² + 30Ā²) = 33.5 m/s
and
uā = sqrt((- 10)Ā² + 5Ā²) = 11.2 m/s
total kinetic energy before collision is given as
KE = (0.5) m uĀ²ā + (0.5) m uĀ²ā Ā = (0.5) (2) (33.5)Ā² + (0.5) (2) (11.2)Ā² = 1247.7 J
similarly final speed after collision is given as
vā = sqrt((- 5)Ā² + (20)Ā²) = 20.6 m/s
vā = sqrt((10)Ā² + (15)Ā²) = 18 m/s
total kinetic energy after collision is given as
KE' = (0.5) m vĀ²ā + (0.5) m vĀ²ā Ā = (0.5) (2) (20.6)Ā² + (0.5) (2) (18)Ā² = 748.4 J
Change in kinetic energy is given as
ĪKE = KE' - KE
inserting the values
ĪKE = 748.4 - 1247.7
ĪKE = - 499.3 J
hence kinetic energy lost comes out to be 499.3 J
