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In projectile motion, the term "horizontal velocity" refers to the constant speed at which a projectile travels horizontally. It's important to note that this velocity does not change throughout the motion, assuming air resistance is negligible. For example, if a projectile is fired from a gun at a speed of \(250\, \text{m/s}\), this value remains unchanged until the projectile hits the ground.
The horizontal component of motion does not affect how long the projectile is in the air or the vertical descent due to gravity. Because there are no horizontal forces acting on the projectile, the horizontal velocity remains consistent:

• Initial horizontal velocity \(v_x = 250\, \text{m/s}\)
• This value remains the same until impact

This concept helps simplify calculations because one can separate vertical and horizontal components of motion when solving projectile problems.

"Time of flight" is the duration in which a projectile remains in the air from the moment it is launched until it strikes the ground. In a projectile problem, this time is usually determined by analyzing the vertical motion, especially when the projectile is launched horizontally.
Here's how you calculate the time of flight using the formula for vertical displacement:

• Start with the equation: \( h = \frac{1}{2}gt^2 \)
• Solve for time \( t \) as it falls from a height of \(45\, \text{m}\)

By plugging in our values \(45 = \frac{1}{2} \times 9.8 \times t^2\), you find \( t \approx 3.03\, \text{s} \).
This tells us that the projectile remains in the air for approximately \(3.03\, \text{seconds}\), irrespective of its horizontal velocity.

Vertical velocity in projectile motion refers to the speed at which the projectile travels upward or downward. When a projectile is launched horizontally, its initial vertical velocity is zero because it doesn't initially move up or down. However, as time progresses, the vertical velocity changes due to the pull of gravity. This is an example of constant acceleration motion.
To find the vertical velocity at impact, use the formula:

• \(v_y = gt\), where \(g = 9.8\, \text{m/s}^2\), and \(t\) is the time of flight.

Given \( t = 3.03\, \text{seconds}\),
Plug these into the equation: \( v_y = 9.8 \times 3.03 \approx 29.7\, \text{m/s}\).
This calculation indicates how fast the projectile is moving vertically downward upon impacting the ground.

"Acceleration due to gravity" is a crucial concept in understanding projectile motion. On Earth, this value is a constant \(9.8\, \text{m/s}^2\), directed downward toward the center of the Earth. This acceleration affects only the vertical component of a projectile's motion, not the horizontal.
Here's why gravity is key in projectile calculations:

• Gravity causes the projectile to accelerate downward, increasing its vertical velocity over time.
• It dictates how long a projectile remains in the air during its time of flight.
• At impact, the vertical velocity is solely dependent on gravity and the time the projectile has been falling.

Thus, understanding gravity allows us to calculate both the time of flight and the final vertical velocity accurately, providing a comprehensive view of the object's motion throughout its trajectory.