The correct answer is C) The object's velocity will remain constant.
1. Impulse is defined as the product of force and time. It is equal to the change in momentum of an object.
- Impulse = force × time
2. The question states that the similar object receives the same impulse for a given time. Since the impulse is the same, the change in momentum of the similar object will also be the same.
3. Momentum is the product of mass and velocity. It is a measure of an object's motion.
- Momentum = mass × velocity
4. Since the change in momentum is the same for both the original object and the similar object, and the force and time are the same, we can set up an equation to compare the two objects:
- (mass of original object) × (change in velocity of original object) = (mass of similar object) × (change in velocity of similar object)
5. Given that the mass of the similar object is half that of the original object, let's say the change in velocity of the original object is Δv. The equation becomes:
- (mass of original object) × Δv = (0.5 × mass of original object) × (change in velocity of similar object)
6. Simplifying the equation, we get:
- Δv = 0.5 × (change in velocity of similar object)
7. This equation tells us that the change in velocity of the similar object will be twice the change in velocity of the original object.
8. However, since both objects are initially moving at the same constant velocity, the final velocities of both objects will still be the same.
Therefore, the answer is C) The object's velocity will remain constant. The change in mass does not affect the final velocity when the same impulse is applied for the same time.