with detailed solving calculate the kinetic energy gained or lost in the collision between two 2.0 kg bodies A and B when the velocities before collision is UA=15i+30j and UB = -10+5.0j after collision VA=-5.0i+20j and VB=10i+15j

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