The  product  of  average  force  and  the  time  it  is  exerted  is  called  the  impulse  of  force.  From Newton's second law

The impulse of force can be extracted and found to be equal to the change in momentum of an object provided the mass is constant:

The change in momentum is in the same direction as the applied impulse.
Thus, angle between themis 0degree.

The impulse-momentum theorem and the angle between the impulse vector and the change in momentum vector

The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse applied to it. Mathematically, this can be expressed as:

Δp = J

Where Δp represents the change in momentum and J represents the impulse.

Understanding the given scenario

In the given scenario, an impulse is applied to a moving object with the force at an angle of 120° with the velocity vector. This means that the force is not in the same direction as the velocity vector. Let's analyze the situation step by step to determine the angle between the impulse vector and the change in momentum vector.

The change in momentum vector

The change in momentum vector can be calculated by subtracting the initial momentum vector from the final momentum vector.

Δp = pf - pi

Since the object is already moving, it has an initial momentum vector pi. The impulse is applied, resulting in a change in momentum Δp. The object's final momentum vector pf can be calculated by adding the initial momentum vector and the change in momentum vector.

The impulse vector

The impulse vector can be calculated using the equation:

J = F * Δt

Where F represents the force applied and Δt represents the time interval over which the force is applied.

In this scenario, the force is applied at an angle of 120° with the velocity vector. Therefore, the impulse vector can be broken down into two components: one along the direction of the velocity vector and one perpendicular to it.

The angle between the impulse vector and the change in momentum vector

Since the impulse vector has two components, one along the direction of the velocity vector and one perpendicular to it, the change in momentum vector can also be broken down into two components along the same directions.

The component of the change in momentum vector along the direction of the velocity vector is responsible for changing the speed of the object, while the component perpendicular to the velocity vector is responsible for changing the direction of the object's velocity.

In this scenario, the force is applied at an angle of 120° with the velocity vector. Since the impulse vector and the force vector are in the same direction, the component of the impulse vector along the direction of the velocity vector will be equal to the component of the force vector along the direction of the velocity vector.

Since the angle between the impulse vector and the change in momentum vector is the same as the angle between the force vector and the velocity vector, which is 0°, the correct answer is option B) 0°.

The angle between the impulse vector and the change in momentum vector can be determined by understanding the definitions of impulse and momentum, as well as their relationship to each other.

1. Impulse:
- Impulse is the product of force and time. It represents the change in momentum of an object.
- Mathematically, impulse (J) is given by the equation J = F * Δt, where F is the force applied and Δt is the time interval over which the force is applied.

2. Momentum:
- Momentum is the product of an object's mass and its velocity. It represents the quantity of motion possessed by the object.
- Mathematically, momentum (p) is given by the equation p = m * v, where m is the mass of the object and v is its velocity.

3. Relationship between impulse and momentum:
- The impulse experienced by an object is equal to the change in its momentum.
- Mathematically, this can be expressed as J = Δp, where J is the impulse and Δp is the change in momentum.

To determine the angle between the impulse vector and the change in momentum vector, we need to consider the given information that the force is applied at an angle of 120° with the velocity vector.

4. Impulse vector:
- The impulse vector can be represented as J = F * Δt, where F is the force vector and Δt is the time interval vector.
- Since the force is applied at an angle of 120° with the velocity vector, the impulse vector will also be at the same angle with the velocity vector.

5. Change in momentum vector:
- The change in momentum vector can be represented as Δp = m * Δv, where m is the mass vector and Δv is the change in velocity vector.
- As the object is already moving, the change in velocity vector will be in the same direction as the velocity vector.
- Therefore, the change in momentum vector will also be in the same direction as the velocity vector.

6. Angle between impulse vector and change in momentum vector:
- Since both the impulse vector and the change in momentum vector are in the same direction as the velocity vector, their angle will be 0°.
- This means that the impulse vector and the change in momentum vector are parallel to each other.

Hence, the correct answer is option B) 0°.