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Gravity is the force that pulls objects toward the earth's surface. It is responsible for the vertical motion of objects when they are in the air. When a baseball is thrown horizontally by a pitcher, gravity starts acting on it immediately. Regardless of the horizontal velocity, the ball experiences an acceleration downward due to gravity, which is a constant at approximately 9.81 m/s².

Understanding the role of gravity is essential in projectile motion problems because it determines how much an object will fall or drop over time. In our example, the effect of gravity is what causes the baseball, thrown horizontally, to drop by approximately 0.843 meters by the time it reaches the catcher.

Key points to remember about gravity in these scenarios include:

• Gravity acts downwards consistently.
• It is constant at 9.81 m/s² near the surface of the Earth.
• Gravity affects only vertical motion, not horizontal.

Horizontal velocity refers to the speed at which an object moves along the horizontal plane. In projectile motion, horizontal velocity remains constant if air resistance is negligible. This is because there are typically no horizontal forces acting on the object once it’s been projected.

In the baseball example, the pitcher throws the ball with a horizontal velocity of 41.0 m/s. This high speed ensures the ball travels quickly across the horizontal distance of 17 meters to the catcher. Since there is no horizontal acceleration (assuming no air resistance), the horizontal velocity remains stable throughout the ball’s flight.

To determine the time of flight for the baseball, we use:

• The formula: \[ t = \frac{d}{v} \]
• The horizontal distance \(d = 17.0 \text{ meters} \)
• The horizontal velocity \(v = 41.0 \text{ m/s} \)

This calculation becomes:\[ t = \frac{17.0}{41.0} \approx 0.4146 \text{ seconds} \]This time figure is crucial for emphasizing how horizontal velocity directly influences the dynamics of projectile motion.

Vertical displacement in projectile motion refers to how far the object has moved vertically from its original position, under the effect of gravity. In our scenario, while the baseball is traveling horizontally, it is simultaneously dropping downwards due to gravity.

The calculation for vertical displacement is based on the time of flight and the acceleration due to gravity. The formula used for calculating the vertical drop is:\[ h = \frac{1}{2}gt^2 \]where:

• \( g = 9.81 \text{ m/s}^2 \) (gravity)
• \( t = 0.4146 \text{ seconds} \) (from the horizontal motion calculation)

Substituting these values, we find the vertical displacement:\[ h = \frac{1}{2} \times 9.81 \times (0.4146)^2 \approx 0.843 \text{ meters} \]
This calculation shows that despite being thrown horizontally, the ball shifts vertically by about 0.843 meters by the time it reaches the catcher, showcasing how vertical displacement occurs in all projectile motion due to gravity.