Hey object of mass 2 kg travelling with a velocity of 10 m/s hits a body of mass 3 kg at rest after eating the first object moving with velocity of 8 m/s find the velocity of second of the drafting

To solve the problem of two objects colliding, we can apply the principle of conservation of momentum. This principle states that the total momentum of a closed system before a collision is equal to the total momentum after the collision, provided no external forces act on it. Let's break down the situation step by step.

Understanding the Scenario

We have two objects involved in the collision:

• Object 1: Mass = 2 kg, Initial Velocity = 10 m/s
• Object 2: Mass = 3 kg, Initial Velocity = 0 m/s (at rest)

After the collision, Object 1 moves with a new velocity of 8 m/s, and we need to find the final velocity of Object 2.

Applying the Conservation of Momentum

The formula for momentum (p) is given by:

p = mass × velocity

Before the collision, the total momentum (p_initial) can be calculated as follows:

p_initial = (mass of Object 1 × velocity of Object 1) + (mass of Object 2 × velocity of Object 2)

Substituting the known values:

p_initial = (2 kg × 10 m/s) + (3 kg × 0 m/s) = 20 kg·m/s

Calculating the Final Momentum

After the collision, the total momentum (p_final) is given by:

p_final = (mass of Object 1 × final velocity of Object 1) + (mass of Object 2 × final velocity of Object 2)

Let’s denote the final velocity of Object 2 as v. Then:

p_final = (2 kg × 8 m/s) + (3 kg × v)

Calculating the momentum of Object 1 after the collision:

p_final = 16 kg·m/s + 3 kg × v

Setting Initial and Final Momentum Equal

According to the conservation of momentum:

p_initial = p_final

Substituting the values we calculated:

20 kg·m/s = 16 kg·m/s + 3 kg × v

Solving for v

Now, we can rearrange the equation to find v:

20 kg·m/s - 16 kg·m/s = 3 kg × v

4 kg·m/s = 3 kg × v

Now, divide both sides by 3 kg:

v = (4 kg·m/s) / (3 kg) = 4/3 m/s

This simplifies to approximately:

v ≈ 1.33 m/s

Final Result

The final velocity of Object 2 after the collision is approximately 1.33 m/s in the direction of the initial motion of Object 1. This demonstrates how momentum is conserved in a collision, allowing us to determine the final velocities of the objects involved.