Projectile Motion of a Tennis Ball

What are the components of velocity, time of flight, and maximum height for a tennis ball in projectile motion with an initial speed of 54.7 m/s and a launch angle of 25°, neglecting air resistance? The question concerns calculating the components of velocity, time of flight, and maximum height for a tennis ball in projectile motion, assuming no air resistance. To calculate the components of the initial velocity, you can use trigonometry: a) Horizontal component of velocity (Vx) = initial speed (V) × cos(θi) b) Vertical component of velocity (Vy) = initial speed (V) × sin(θi) To determine the time of flight and maximum height, you can use the kinematic equations for projectile motion: c) Time of flight (T) = (2 × Vy) / g, where g is the acceleration due to gravity d) Maximum height (H) = (Vy²) / (2g) By plugging in the given values of an initial speed of 54.7 m/s and a launch angle of 25°, we can solve for the components of velocity, time of flight, and maximum height for the tennis ball.

Projectile motion involves the motion of an object in two dimensions under the influence of gravity, with no other forces affecting its trajectory. In this scenario, a tennis ball is launched with an initial speed of 54.7 m/s at an angle of 25° above the horizontal. Let's break down the calculations for each component and parameter:

a) Horizontal Component of Velocity (Vx):

The horizontal component of velocity represents the speed of the tennis ball in the horizontal direction. Using the trigonometric relationship:

Vx = V × cos(θi)

Substitute the given values:

Vx = 54.7 m/s × cos(25°)

Calculating this, we get the horizontal component of velocity for the tennis ball.

b) Vertical Component of Velocity (Vy):

The vertical component of velocity indicates the speed of the tennis ball in the vertical direction. By applying the trigonometric formula:

Vy = V × sin(θi)

Substitute the known values:

Vy = 54.7 m/s × sin(25°)

Through this calculation, we find the vertical component of velocity for the tennis ball.

c) Time of Flight (T):

The time of flight refers to the total time taken by the tennis ball to complete its trajectory. Using the kinematic equation for time of flight:

T = (2 × Vy) / g

Where g is the acceleration due to gravity. By substituting the calculated vertical component of velocity and the acceleration due to gravity (usually 9.81 m/s²), we can determine the time of flight for the tennis ball.

d) Maximum Height (H):

The maximum height signifies the highest point reached by the tennis ball during its flight. According to the kinematic equation for maximum height:

H = (Vy²) / (2g)

Plugging in the vertical component of velocity and the acceleration due to gravity allows us to compute the maximum height attained by the tennis ball.

By performing these calculations, we can provide the components of velocity (horizontal and vertical), time of flight, and maximum height for the tennis ball in projectile motion. Additional factors such as air resistance would impact these values, but in this case, we have disregarded its influence for simplicity.

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