91Ó°ÊÓ

Horizontal motion is an essential element of projectile motion, as it refers to the motion of an object in the horizontal direction, without any influence from vertical forces like gravity. In this exercise, the bullet's horizontal motion determines how long it travels before reaching the target. With a speed of 460 m/s and a target distance of 45.7 meters, we calculate its horizontal time of flight using the formula:

• Time of flight: \( t = \frac{d}{v} \)
• Where \(d\) is the distance (45.7 m) and \(v\) is the velocity (460 m/s)

This gives us the time it takes for the bullet to reach the target: approximately 0.09913 seconds. Understanding horizontal motion helps us figure out other aspects of projectile motion like vertical displacement.

Vertical displacement involves understanding how much an object falls or ascends when moving upward or downward, respectively. In projectile motion, vertical displacement is influenced by gravity. Even though the bullet is initially fired horizontally, gravity pulls it downward as it moves towards the target.To calculate the vertical drop of the bullet, we employ the formula:

• Vertical displacement \( h = \frac{1}{2}gt^2 \)
• Where \(g\) is the gravitational acceleration (9.81 m/s²) and \(t\) is the time of flight (0.09913 s)

Through this, we find the vertical displacement to be approximately 0.048 meters. This means that the bullet drops 0.048 meters while it travels horizontally to the target point.

Gravitational acceleration is the constant force acting on objects pulling them towards the Earth's center. It is vital to know that regardless of the horizontal speed, gravity always affects vertical motion. In our calculations, we use the standard value of gravitational acceleration:

• \( g = 9.81 \text{ m/s}^2 \)

This factor is critical when determining how far a projectile will drop during its flight. By applying this constant to the formula for vertical displacement \( h = \frac{1}{2}gt^2 \), we can precisely predict how the projectile behaves as it travels. Understanding gravitational acceleration helps us align our aim to ensure the bullet meets its intended path, compensating for the drop observed in flight.

The time of flight refers to the duration a projectile remains in motion from its initial launch until it reaches its target. In this exercise, the time of flight for the bullet ensures that it has enough duration to traverse the 45.7-meter distance horizontally. Using the horizontal motion equation, we calculated the time of flight to be approximately 0.09913 seconds. Knowing the time of flight allows us to predict other factors of the projectile's path, like vertical displacement, since:

• Vertical displacement directly depends on the time of flight.

Thus, everything in projectile motion is interconnected, with the time of flight serving as a crucial measure to calculate overall motion dynamics.