A 1500 kg car traveling at 100 km/h west collides with a 1200 kg car traveling east at 85 km/h. The heavier car slows to 25 km/h after the collision. How fast is the lighter car traveling after the two cars collide?

100km/h = 100,000m/3600s = 27.8 m/s.

85km/h = 85,000m/3600s = 23.6 m/s.
25km/h = 25,000m/3600s = 6.94 m/s.

M1*V1 + M2*V2 = M1*V3 + M2*V4.
1500*(-27.8)+1200*23.6=1500*(-6.9)+1200V
Solve for V.

To solve this problem, we can apply the principle of conservation of momentum.

1. First, let's calculate the initial momentum of each car before the collision. Momentum is calculated as the product of mass and velocity:

Momentum of the heavier car (1500 kg) = mass × velocity
= 1500 kg × 100 km/h

Momentum of the lighter car (1200 kg) = mass × velocity
= 1200 kg × (-85 km/h) [Since it is traveling in the opposite direction]

Note: We take the negative sign for the velocity of the lighter car because it is traveling in the opposite direction.

2. Now, let's calculate the final momentum of the system after the collision. The heavier car slows down to 25 km/h, and the velocity of the lighter car after the collision is unknown.

Final momentum of the system = momentum of the heavier car + momentum of the lighter car

According to the principle of conservation of momentum, the final momentum of the system is equal to the initial momentum of the system.

Before the collision, the total momentum of the system is zero since the cars are traveling in opposite directions.

Therefore, we have:

0 = (momentum of the heavier car) + (momentum of the lighter car)

3. Now, let's calculate the momentum of the heavier car after the collision. We can use the new velocity given in the question.

Momentum of the heavier car (after the collision) = mass × velocity
= 1500 kg × 25 km/h

4. We can substitute the values into the equation we formulated in step 2:

0 = (1500 kg × 100 km/h) - (1200 kg × (-85 km/h)) + (1500 kg × 25 km/h) + (momentum of the lighter car)

Simplifying the equation:
0 = 150000 kg·km/h + 102000 kg·km/h + 37500 kg·km/h + (momentum of the lighter car)

We can add the terms on the left side of the equation together:

0 = 289500 kg·km/h + (momentum of the lighter car)

5. To find the momentum of the lighter car, we need to solve the equation for it.

momentum of the lighter car = -289500 kg·km/h

6. Finally, let's find the velocity of the lighter car after the collision. We can calculate this by dividing the momentum by the mass of the lighter car.

velocity of the lighter car (after the collision) = momentum of the lighter car / mass of the lighter car

Let's substitute the values into the equation:

velocity of the lighter car = (-289500 kg·km/h) / 1200 kg

Simplifying the equation:

velocity of the lighter car ≈ -241.25 km/h

Therefore, the velocity of the lighter car after the collision is approximately 241.25 km/h, traveling in the east direction.

To find the velocity of the lighter car after the collision, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

Momentum = mass × velocity

Let's assign directions to the velocities: west as positive (+) and east as negative (-).

The momentum before the collision can be calculated as:
Momentum before = (mass of the first car × velocity of the first car) + (mass of the second car × velocity of the second car)

Momentum before = (1500 kg × 100 km/h) + (1200 kg × (-85 km/h))
= (1500 kg × 27.778 m/s) + (1200 kg × (-23.611 m/s))

Now, let's assign the velocity of the lighter car after the collision as "v" (unknown).

The momentum after the collision can be calculated as:
Momentum after = (mass of the first car × velocity of the first car after collision) + (mass of the second car × velocity of the second car after collision)

Momentum after = (1200 kg × v) + (1500 kg × 25 km/h)
= (1200 kg × v) + (1500 kg × 6.944 m/s)

According to the principle of conservation of momentum, the momentum before the collision should equal the momentum after the collision.

Therefore, we can set up an equation:

Momentum before = Momentum after

(1500 kg × 27.778 m/s) + (1200 kg × (-23.611 m/s)) = (1200 kg × v) + (1500 kg × 6.944 m/s)

Now, let's solve for v:

41475 kg·m/s - 28333 kg·m/s = 1200 kg·v + 10416 kg·m/s

13142 kg·m/s = 1200 kg·v + 10416 kg·m/s

1200 kg·v = 13142 kg·m/s - 10416 kg·m/s

1200 kg·v = 2730 kg·m/s

Dividing both sides by 1200 kg:

v = 2730 kg·m/s ÷ 1200 kg

v ≈ 2.275 m/s

Therefore, after the collision, the lighter car is traveling at approximately 2.275 meters per second in the west direction.

Ur mum