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