Conservation Of Momentum

We will use the principle of conservation of momentum. The total momentum before firing is zero, and the total momentum after firing must also be zero (since no external force is acting on the system). Let: - (mass of the bullet) - (speed of the bullet) - (mass of the gun) - (recoil velocity of the gun) Using conservation of momentum: Thus, the recoil speed of the gun is 0.25 m/s in the opposite direction. Thus, the correct answer is (B) 0.25.

The change in momentum is given by: where , , and (since the direction is reversed). Substituting the values: The average force is given by: Thus, the average force is 1,200 N (positive direction).

In a collision where two particles move together after impact, kinetic energy is not conserved, but momentum is conserved. This type of collision is called an inelastic collision. In a perfectly elastic collision, both kinetic energy and momentum are conserved, while in an inelastic collision, only momentum is conserved. Thus, the correct answer is Inelastic.

Impulse is equal to change in momentum: Take initial velocity toward the wall as positive: After rebound, the direction reverses: So, Magnitude of impulse:
Hence, the correct answer is:

Step 1: Understanding the Concept:
Impulse ( ) is defined as the force integrated over time, which according to the impulse-momentum theorem, is exactly equal to the change in momentum ( ) of the object. Momentum is a vector quantity, so direction matters critically.
Step 2: Key Formula or Approach:

Define a coordinate system. Let the direction towards the wall be positive.
Step 3: Detailed Explanation:
Given values:
Mass of ball, kg
Initial speed towards wall, m/s
Final speed rebounding from wall, m/s
Let's assign vector signs based on our coordinate system (towards wall = +):
Initial velocity vector, m/s
Final velocity vector, m/s (it reversed direction)
Now, calculate the initial and final momentum:
Initial momentum, kg m/s
Final momentum, kg m/s
Calculate Impulse:



The negative sign indicates the impulse is directed away from the wall, which makes sense as the wall exerts force outward to stop and reverse the ball.
Usually, questions ask for the magnitude of the impulse.
Magnitude of Impulse = N s.
Step 4: Final Answer:
The magnitude of the impulse is 39.6 N s.