A tennis ball is struck and departs from the racket horizontally with a speed of 26.9 m/s. The ball hits the court at a horizontal distance of 18.1 from the racket. How far above the court is the tennis ball when it leaves the racket?

d = V*T.

d = 26.9 * T = 18.1 m
T = 0.67 s.

h = 0.5g*t^2 = 4.9*(0.67)^2 = 2.22 m.

To determine how far above the court the tennis ball is when it leaves the racket, we can use the principles of projectile motion.

Let's consider the horizontal and vertical components of motion separately:

1. Horizontal motion: The ball is struck with a horizontal speed of 26.9 m/s. Since there are no horizontal forces acting on the ball, its horizontal velocity remains constant throughout its flight. Therefore, the time taken for the ball to travel horizontally (from the racket to the point where it hits the ground) can be calculated using the equation:

time = distance / speed
time = 18.1 m / 26.9 m/s

2. Vertical motion: The ball is initially at a height above the court and then falls due to the force of gravity. We need to find the vertical distance the ball travels before hitting the ground.

Let's denote the initial height as h. The time taken for the ball to fall can be calculated using the formula:

time = √(2h / g)

where g is the acceleration due to gravity (approximately 9.8 m/s²).

Now, since the time taken for the ball to travel horizontally is the same as the time taken for it to fall vertically, we can equate the two equations for time:

18.1 m / 26.9 m/s = √(2h / 9.8 m/s²)

Solving this equation will give us the value of h, the initial height above the court.

First, let's calculate the time taken for the ball to travel horizontally:

time = 18.1 m / 26.9 m/s
time ≈ 0.673 seconds

Now, let's square both sides of the equation and solve for h:

(18.1 m / 26.9 m/s)² = 2h / 9.8 m/s²
(0.673 s)² = 2h / 9.8
0.453029 s² = 2h / 9.8

Cross multiplying:

2h = 9.8 * 0.453029 s²
h = (9.8 * 0.453029) / 2
h ≈ 2.134 meters

Therefore, the tennis ball is approximately 2.134 meters above the court when it leaves the racket.