I WIL A 2.00-kg object traveling east at 20.0 m/s collides with a 3.00-kg object traveling west at 10.0 m/s. After the collision, the 2.00-kg object has a velocity 5.00 m/s to the west. How much kinetic energy was lost during the collision? ...

Using the following given values:

Object 1:

Mass = M1 = 2 kg

Velocity before collision = Vb1 = 20 m/s

Velocity after collision = Va1 = - 5 m/s

Object 2:

Mass = M2 = 3 kg

Velocity before collision = Vb2 = - 10 m/s

Velocity after collision = Va2 = ? m/s

Obtaining Va2 via law of conservation of momentum:

total momentum after collision = total momentum before collision

M1 * Va1 + M2 * Va2 = M1 * Vb1 + M2 * Vb2

2*-5 + 3Va2 = 2*20 + 3*-10

Va2 = 6.67

Total kinetic energy before collision:

KE1 = (1/2) * M1*Vb1^2 + (1/2) * M2*Vb2^2

KE1 = (1/2) * 2 * (20) ^2 + (1/2) * 3 * (-10) ^2

KE1 = 550 J

Total kinetic energy after collision:

KE2 = (1/2) * M1*Va1^2 + (1/2) * M2*Va2^2

KE2 = (1/2) * 2 * (-5) ^2 + (1/2) * 3 * (6.67) ^2

KE2 = 91.73 J

Total kinetic energy lost:

Energy lost = KE1 - KE2 = 550 - 91.73 = 458.27 J