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Impulse is a pivotal concept when studying dynamics, particularly when it comes to how forces influence the motion of objects. Essentially, impulse quantifies the effect of a force acting over a period. The formula for impulse is expressed as \( \vec{I} = \vec{F} \times \Delta t \), where:

• \( \vec{I} \) represents impulse, a vector quantity that reflects how the force changes the object's momentum.
• \( \vec{F} \) is the net force applied to the object.
• \( \Delta t \) signifies the time duration for which the force is applied.

By merging force and time, impulse provides the magnitude and direction of the change in momentum. It's crucial to recognize that while force might be large, a minimal time span reduces the overall impulse, potentially leading to small changes in velocity. Conversely, prolonged application of even a small force can result in significant motion changes. Understanding the impulse formula is critical for calculating how external forces can alter the motion of objects in a specified direction.

Net force is the total force acting on an object, resulting from the combination of all individual forces. It plays a crucial role in determining how an object's motion changes. In this context, the net force acting on the tennis ball has two components: \( -(380 N)\hat{\imath} \) in the x-direction and \( (110 N)\hat{\jmath} \) in the y-direction.
This concept essentially sums up all forces to give a single resultant force that influences the object's state of motion.

• If the net force is non-zero, the object experiences an acceleration, reflecting a change in its speed or direction.
• Alternatively, a net force of zero means the object maintains its present state of motion, be it rest or uniform motion.

Net force influences the object's momentum, and hence tying it directly to the impulse experienced due to the force applied over a given duration.

Change in velocity is a direct consequence of the impulses exerted on an object, as dictated by the net force and time. This results in an alteration of the object's speed or direction. The relationship between impulse and this change is mathematically described using impulse-momentum theorem: \( m\Delta\vec{v} = \vec{I} \) where:

• \( m \) is the mass of the object, calculated by dividing the weight of the tennis ball (0.560 N) by gravity (9.81 m/s²), yielding approximately 0.0571 kg.
• \( \Delta\vec{v} \) is the change in velocity, derived from calculating the impulse in both x and y components and dividing by the mass.

Through changes in the net force or its application duration, velocity components along different axes of the object can be distinctly altered.
For the tennis ball, as calculated, a change of \( -19.97 \text{ m/s} \) in the x-direction and \( 5.78 \text{ m/s} \) in the y-direction occurs. Understanding how velocity changes underpins much of classical mechanics by describing the motion resulting from external forces applied to an object over time.