given that :
UA=15i+30j and UB =-10+5.0j
speed before collision is given as
u₁ = sqrt(15² + 30²) = 33.5 m/s
and
u₂ = sqrt((- 10)² + 5²) = 11.2 m/s
total kinetic energy before collision is given as
KE = (0.5) m u²₁ + (0.5) m u²₂ = (0.5) (2) (33.5)² + (0.5) (2) (11.2)² = 1247.7 J
similarly final speed after collision is given as
v₁ = sqrt((- 5)² + (20)²) = 20.6 m/s
v₂ = sqrt((10)² + (15)²) = 18 m/s
total kinetic energy after collision is given as
KE' = (0.5) m v²₁ + (0.5) m v²₂ = (0.5) (2) (20.6)² + (0.5) (2) (18)² = 748.4 J
Change in kinetic energy is given as
ΔKE = KE' - KE
inserting the values
ΔKE = 748.4 - 1247.7
ΔKE = - 499.3 J
hence kinetic energy lost comes out to be 499.3 J
