A car (mass = 1100 kg) is traveling at 32 m/s when it collides head-on with a sport utility vehicle (mass= 2500 kg) traveling in the opposite direction. In the collision, the two vehicles come to a halt. At what speed was the sport utility vehicle traveling?

Options

A. 11 m/s
B. 14 m/s
C. 16 m/s
D. 18 m/s

Answer

To solve the problem, we will use the principle of conservation of momentum. The momentum before the collision must equal the momentum after the collision. Since the two vehicles come to a halt after the collision, the final momentum is zero.

### Step-by-Step Solution:

1. **Identify the Masses and Velocities:**
- Mass of the car (m₁) = 1100 kg
- Velocity of the car (v₁) = 32 m/s (moving in the positive direction)
- Mass of the sport utility vehicle (m₂) = 2500 kg
- Velocity of the sport utility vehicle (v₂) = ? (moving in the negative direction)

2. **Set Up the Momentum Conservation Equation:**
The total momentum before the collision is equal to the total momentum after the collision. Since both vehicles come to a halt after the collision, the final momentum is zero.

\[ m₁ v₁ + m₂ v₂ = 0 \]

3. **Substitute the Known Values:**
Substitute the values of m₁, v₁, and m₂ into the equation:

\[ 1100 \times 32 + 2500 \times v₂ = 0 \]

4. **Calculate the Momentum of the Car:**
Calculate the momentum of the car:

\[ 1100 \times 32 = 35200 \, \text{kg m/s} \]

5. **Rearrange the Equation to Solve for v₂:**
Now, rearranging the equation to find v₂:

\[ 35200 + 2500 v₂ = 0 \]
\[ 2500 v₂ = -35200 \]
\[ v₂ = \frac{-35200}{2500} \]

6. **Calculate v₂:**
Perform the division:

\[ v₂ = -14.08 \, \text{m/s} \]

The negative sign indicates that the sport utility vehicle was traveling in the opposite direction.

### Final Answer:
The speed of the sport utility vehicle was approximately **14.08 m/s**.