A truck of mass 500 kg moving at 4 m/s collides with another truck of mass 1500 kg moving in the same direction at 2 m/s. What is their common velocity just after the collision if they move off together ?

Answer

To find the common velocity of the two trucks after they collide and move off together, we can use the principle of conservation of momentum. Here’s how to solve the problem step by step:

### Step 1: Identify the masses and velocities of the trucks
- Mass of Truck A (m₁) = 500 kg
- Velocity of Truck A (v₁) = 4 m/s
- Mass of Truck B (m₂) = 1500 kg
- Velocity of Truck B (v₂) = 2 m/s

### Step 2: Calculate the momentum before the collision
The momentum (p) of an object is given by the formula:
\[ p = m \times v \]

- Momentum of Truck A (p₁):
\[ p₁ = m₁ \times v₁ = 500 \, \text{kg} \times 4 \, \text{m/s} = 2000 \, \text{kg m/s} \]

- Momentum of Truck B (p₂):
\[ p₂ = m₂ \times v₂ = 1500 \, \text{kg} \times 2 \, \text{m/s} = 3000 \, \text{kg m/s} \]

### Step 3: Calculate the total momentum before the collision
Total momentum before the collision (P_initial):
\[ P_{\text{initial}} = p₁ + p₂ = 2000 \, \text{kg m/s} + 3000 \, \text{kg m/s} = 5000 \, \text{kg m/s} \]

### Step 4: Calculate the total mass after the collision
When the two trucks collide and move off together, their combined mass (M) is:
\[ M = m₁ + m₂ = 500 \, \text{kg} + 1500 \, \text{kg} = 2000 \, \text{kg} \]

### Step 5: Apply the conservation of momentum
According to the law of conservation of momentum:
\[ P_{\text{initial}} = P_{\text{final}} \]
Where \( P_{\text{final}} = M \times V \) (V is the common velocity after the collision).

### Step 6: Set up the equation
\[ P_{\text{initial}} = M \times V \]
\[ 5000 \, \text{kg m/s} = 2000 \, \text{kg} \times V \]

### Step 7: Solve for the common velocity (V)
To find V, rearrange the equation:
\[ V = \frac{5000 \, \text{kg m/s}}{2000 \, \text{kg}} = 2.5 \, \text{m/s} \]

### Final Answer
The common velocity of the two trucks just after the collision is **2.5 m/s**.

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