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Projectile motion is a form of motion experienced by an object that is launched into the air and moves under the influence of gravity. A key aspect of projectile motion is that the object travels along a curved trajectory called a parabola. For any projectile, such as a football in this exercise, it has two main components:

• Horizontal component: This is the movement parallel to the Earth's surface. It remains constant, assuming no air resistance.
• Vertical component: This is the movement perpendicular to the Earth, influenced by gravity, which causes the projectile to accelerate downwards.

When solving projectile motion problems, it's important to analyze these components separately to find overall displacement, velocity, and time of flight. This makes it easier to apply physics concepts and formulas.

Displacement in physics refers to the change in position of an object from its starting point to its final position. Unlike distance, which takes into account the entire path traveled, displacement considers only the shortest route between two points—it is a vector quantity. This means it has both magnitude and direction.For the football in this exercise, the net displacement includes both horizontal and vertical movements:

• Horizontal: The ball travels 90 feet across the field.
• Vertical: The ball moves up 10 feet to hit the crossbar.

To find the net displacement, use the Pythagorean theorem on these components, as they form a right triangle. The formula \[ d = \sqrt{(horizontal)^2 + (vertical)^2} \]is utilized, resulting in a displacement of approximately 90.55 feet.By understanding displacement, you can better grasp how far out of position something ends up after a journey.

Average velocity is a measure of the total displacement over the time it takes to make that displacement. It is a vector quantity, meaning it has direction and magnitude, which distinguishes it from average speed (a scalar quantity). In formulaic terms, average velocity is given by:\[ v_{avg} = \frac{\text{displacement}}{\text{time}} \]In this particular case, we had calculated the displacement to be about 90.55 feet, and it took the football 2.50 seconds to reach the crossbar. Thus, the football's average velocity is approximately 36.22 feet per second. It's important to realize that average velocity considers only the starting and finishing points, not the path taken, so it does not fully describe movement where the path isn't straight.

Unit conversion is crucial in physics, allowing different units of measurement to be standardized, ensuring consistency and simpler calculations. Converting between units is often necessary, especially when dealing with problems involving vector quantities like displacement or velocity.In this exercise, the field goal attempt was originally given in yards. The challenge required converting this measurement into feet to match the units used for the vertical height of the crossbar. Since there are 3 feet in a yard, the conversion was:\[ 30 \text{ yards} = 30 \times 3 = 90 \text{ feet} \]This step is vital for accurate calculations—mismatched units can lead to incorrect measurements and results. Mastering unit conversions will help you efficiently solve physics problems and handle data correctly.