91Ó°ÊÓ

Horizontal velocity is the speed at which an object moves along a horizontal path. In projectile motion, this velocity remains constant as long as there is no air resistance.
In our exercise, the tennis ball is struck, and it departs from the racket with a horizontal velocity of 28.0 meters per second.
This means that throughout its flight until it lands, the ball maintains this velocity in the horizontal direction. Hence, the horizontal velocity is crucial for calculating the time of flight when you have the horizontal distance traveled by the object.

• Formula: Horizontal distance = Horizontal velocity × Time of flight.
• In this case: 19.6 m = 28.0 m/s × Time, solving gives Time ≈ 0.7 seconds.

Understanding horizontal velocity helps to predict how far an object can travel across a flat surface while taking gravity into account for the vertical displacement.

The time of flight is the total time an object stays in the air during its motion. For a projectile moving horizontally, like the tennis ball in our problem, it is significant because it determines how long the ball remains airborne before hitting the ground.
In the exercise, we calculated the time of flight by using the horizontal velocity and the horizontal distance traveled:

• Using the formula: \( t = \frac{d}{v_x} \), we have \( t = \frac{19.6 \, ext{m}}{28.0 \, ext{m/s}} \approx 0.7 \, ext{s} \)

This shows that the tennis ball was airborne for approximately 0.7 seconds. Understanding the time of flight helps us to calculate vertical displacement, and see how far the ball has fallen vertically during its flight.

Vertical motion describes how an object moves upward or downward due to gravity. In our exercise, this motion is influenced by the time of flight and gravity. Even though the tennis ball starts with only horizontal velocity, it falls vertically due to gravity.
Using the formula:

• \( h = \frac{1}{2} g t^2 \), where \( g = 9.8 \, ext{m/s}^2 \) is the acceleration due to gravity, we substitute \( t = 0.7 \, ext{s} \).

Calculating, we get \( h = \frac{1}{2} \times 9.8 \times (0.7)^2 \approx 2.4 \, ext{m} \)
This calculation gives us the vertical distance the ball has fallen, which also represents how high it was initially above the court. It's crucial to connect the time of flight with vertical motion to understand how high an object starts above the ground.

Acceleration due to gravity is a constant force that pulls objects towards the Earth. It affects the vertical motion of any object in projectile motion, like our tennis ball example. This acceleration is approximately 9.8 meters per second squared.
It is the key factor that changes the vertical motion of an object flying through the air, despite the constant horizontal velocity.

• When we calculate vertical displacement using gravity's acceleration, it shows us how quickly gravity pulls the object downward.
• This pulling effect results in a parabolic trajectory for projectiles.

Without considering gravity, calculations of a projectile's vertical movement could not be achieved accurately. Therefore, it's vital to learn about gravity's role in altering vertical motion and creating a predictable path for projectiles.