A 1000 kg car travelling at 25m/s south collides head-on with a 2250 kg car travelling at 10m/s in the opposite direction. They stick together after collision. Which way does the wreckage move? What is their final velocity?

i don't know teacher?

m1 = 1000kg

vi1 = -25m/s
m2 = 2250kg
vi2 = 10m/s
vf = ? m/s
(m1*vi1)+(m2*vi2)=(m1+m2)vf
vf=[(m1*vi1)+(m2*vi2)]/ [m1+m2]
vf=[(1000*-25)+(2250*10)]/[1000+2250]
vf = -0.769m/s OR vf = 0.769m/s south

To determine the direction of the wreckage after the collision and the final velocity, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.

Momentum (p) is calculated by multiplying the mass (m) of an object by its velocity (v). In this case, the momentum before the collision is:

Momentum of the 1000 kg car = (mass of 1000 kg) × (velocity of 25 m/s south)
= 1000 kg × (-25 m/s) (since it's moving south)

Momentum of the 2250 kg car = (mass of 2250 kg) × (velocity of 10 m/s)
= 2250 kg × (10 m/s)

Now, to calculate the total momentum before the collision, we add these two momentum values together:

Total momentum before collision = (1000 kg × (-25 m/s)) + (2250 kg × 10 m/s)

To simplify the calculation, let's assign the direction of the south as negative (-) and north as positive (+). So, the equation becomes:

Total momentum before collision = (-25000 kg·m/s) + (22500 kg·m/s)
= -25000 kg·m/s + 22500 kg·m/s
= -2500 kg·m/s

Since momentum is a vector quantity, the negative sign implies that the total momentum before the collision is directed towards the south.

After the collision, the two objects stick together, and their masses combine. The total mass after the collision is:

Total mass after collision = mass of the 1000 kg car + mass of the 2250 kg car
= 1000 kg + 2250 kg
= 3250 kg

To find the final velocity, we divide the total momentum after the collision by the total mass after the collision:

Final velocity = (Total momentum before collision) / (Total mass after collision)
= (-2500 kg·m/s) / (3250 kg)
≈ -0.769 m/s

The negative sign again implies that the wreckage moves in the south direction (opposite to the initial direction of the 1000 kg car).

So, the wreckage moves southward, and the final velocity of the combined wreckage is approximately -0.769 m/s.