A 3 kg toy car with a speed of 10 m/s collides head-on with a 2 kg car traveling in the opposite direction with a speed of 3 m/s. If the cars are locked together after the collision with a speed of 4.80 m/s, how much kinetic energy is lost?

find the velocity after collision:

3*10+2*(-3)=((3+2)V

V=(30-6)/5=5m/s

KE= 1/2 m v^2=1/2 (5)(25)=75/2 Joules

What was the starting energy?
1/2 (3*100)+1/2*2*9=159Joules
check my math.

To calculate the kinetic energy lost in the collision, we need to find the initial and final kinetic energies of the system.

1. Find the initial kinetic energy (KE) of the system:
The formula for kinetic energy is KE = 1/2 * mass * velocity^2.

For the 3 kg car:
KE1 = 1/2 * 3 kg * (10 m/s)^2 = 150 J (Joules).

For the 2 kg car:
KE2 = 1/2 * 2 kg * (3 m/s)^2 = 9 J.

The total initial kinetic energy of the system is the sum of the individual kinetic energies:
Total Initial KE = KE1 + KE2 = 150 J + 9 J = 159 J.

2. Find the final kinetic energy of the system:
The formula for kinetic energy is KE = 1/2 * mass * velocity^2.

After the collision, the two cars lock together and move with a speed of 4.80 m/s.

The total mass of the system is 3 kg + 2 kg = 5 kg.
KEfinal = 1/2 * 5 kg * (4.80 m/s)^2 = 57.6 J.

3. Calculate the kinetic energy lost:
Kinetic energy lost = Total Initial KE - KEfinal.
Kinetic energy lost = 159 J - 57.6 J = 101.4 J.

Therefore, the kinetic energy lost in the collision is 101.4 Joules.

To determine the kinetic energy lost in this collision, we need to calculate the initial and final total kinetic energies of the system, which includes both cars.

1. Calculate the initial total kinetic energy:
The initial total kinetic energy is equal to the sum of the individual kinetic energies of each car before the collision.

Given:
- Mass of the first car (m1) = 3 kg
- Speed of the first car (v1) = 10 m/s
- Mass of the second car (m2) = 2 kg
- Speed of the second car (v2) = 3 m/s

The formula for kinetic energy is: KE = 0.5 * mass * (speed)^2

The initial total kinetic energy (KE_initial) is equal to the sum of the kinetic energies of the two cars before the collision:

KE_initial = 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2

Plugging in the values, we have:
KE_initial = 0.5 * 3 * (10^2) + 0.5 * 2 * (3^2)

2. Calculate the final total kinetic energy:
The final total kinetic energy is equal to the kinetic energy of the system after the collision.
Given:
- Mass of the combined cars after the collision = m1 + m2 = 3 kg + 2 kg = 5 kg
- Speed of the combined cars after the collision (vf) = 4.80 m/s

The final total kinetic energy (KE_final) is given by:
KE_final = 0.5 * (m1 + m2) * vf^2

Plugging in the values, we have:
KE_final = 0.5 * 5 * (4.80^2)

3. Calculate the kinetic energy lost:
The kinetic energy lost in the collision is the difference between the initial and final kinetic energies:

KE_lost = KE_initial - KE_final

Plugging in the values calculated in steps 1 and 2, we can now compute the answer.