An SUV with a mass of 1.80×103 kg is travelling eastbound with a speed of +15.0 m/s,

while a compact car with a mass of 9.00×102 kg is travelling westbound at -15.0 m/s.
The vehicles collide head-on and stick together. What is the speed of the wreck
immediately after the collision, and which way does it move?

To determine the speed of the wreck immediately after the collision and the direction it moves, we can apply the principles of conservation of momentum.

1. Calculate the momentum before the collision:
The momentum of an object is calculated by multiplying its mass by its velocity. The momentum of the SUV (eastbound) before the collision is given by: momentum_suv = mass_suv * velocity_suv = (1.80×103 kg) * (+15.0 m/s) = +2.70×104 kg·m/s (since east direction is positive). Similarly, the momentum of the compact car (westbound) before the collision is: momentum_car = mass_car * velocity_car = (9.00×102 kg) * (-15.0 m/s) = -1.35×104 kg·m/s (since west direction is negative).

2. Apply the conservation of momentum:
The total momentum before the collision is equal to the total momentum after the collision, since no external forces act on the system. Therefore, the momentum of the wreck immediately after the collision is: momentum_wreck = momentum_suv + momentum_car = (+2.70×104 kg·m/s) + (-1.35×104 kg·m/s) = +1.35×104 kg·m/s.

3. Calculate the speed of the wreck:
The mass of the SUV and the compact car are combined as they stick together after the collision. Therefore, the mass of the wreck is: mass_wreck = mass_suv + mass_car = (1.80×103 kg) + (9.00×102 kg) = 2.70×103 kg. Substitute the mass and momentum values into the equation for momentum to solve for the wreck's speed: momentum_wreck = mass_wreck * velocity_wreck. Rearranging the equation gives: velocity_wreck = momentum_wreck / mass_wreck = (+1.35×104 kg·m/s) / (2.70×103 kg) = +5.0 m/s.

4. Determine the direction of the wreck's movement:
Since the resulting velocity of the wreck is positive (+5.0 m/s), it indicates that the wreck is moving in the eastbound direction, the same direction as the initial velocity of the SUV.

Therefore, the speed of the wreck immediately after the collision is 5.0 m/s in the eastbound direction.

To find the speed of the wreck immediately after the collision, we will 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. The momentum of an object is given by the product of its mass and velocity.

Given:
Mass of SUV (m1) = 1.80×10^3 kg
Velocity of SUV (v1) = +15.0 m/s (east)
Mass of compact car (m2) = 9.00×10^2 kg
Velocity of compact car (v2) = -15.0 m/s (west)

Step 1: Calculate the momentum of the SUV before the collision.
Momentum of SUV before collision = mass of SUV × velocity of SUV
= (1.80×10^3 kg) × (+15.0 m/s)
= +2.70×10^4 kg·m/s (east)

Step 2: Calculate the momentum of the compact car before the collision.
Momentum of compact car before collision = mass of compact car × velocity of compact car
= (9.00×10^2 kg) × (-15.0 m/s)
= -1.35×10^4 kg·m/s (west)

Step 3: Calculate the total momentum before the collision.
Total momentum before collision = momentum of SUV before collision + momentum of compact car before collision
= (+2.70×10^4 kg·m/s) + (-1.35×10^4 kg·m/s)
= +1.35×10^4 kg·m/s (east - west)

Step 4: Since the two vehicles stick together after the collision, we can assume that the final velocity of the wreck is the same as the total momentum before the collision divided by the total mass of the vehicles.

Total mass of the vehicles = mass of SUV + mass of compact car
= 1.80×10^3 kg + 9.00×10^2 kg
= 2.70×10^3 kg

Step 5: Calculate the velocity of the wreck (final velocity).
Velocity of the wreck (final velocity) = total momentum before collision / total mass of the vehicles
= (+1.35×10^4 kg·m/s) / (2.70×10^3 kg)
= +5.00 m/s (east - west)

So, the speed of the wreck immediately after the collision is 5.00 m/s, and it moves towards the east-west direction.

m₁v₁ - m₂v₂ =(m₁+m₂)u

u= (m₁v₁ - m₂v₂)/(m₁+m₂)=
=(1.8•10³•15-9•10²•15)/(1.8•10³+9•10²)=
=13500/2700=5 m/s (eastbound)