Final answer:
To calculate the height from which a tennis ball is struck horizontally with a given speed and distance, we find the time of flight by dividing the distance by speed, and then use this time to calculate the vertical displacement due to gravity, yielding a height of approximately 2.41 meters.
Step-by-step explanation:
The question is asking to calculate the height from which a tennis ball is struck given its horizontal displacement and initial speed, assuming a horizontal launch. We know the ball travels a horizontal distance of 20.4 m with a horizontal speed of 29.1 m/s. Using the kinematic equations for projectile motion, we can find the time it takes for the ball to travel this distance by dividing the horizontal distance by the horizontal speed.
t = distance / speed = 20.4 m / 29.1 m/s ≈ 0.701 s
Now, since the ball departs horizontally, the initial vertical velocity is 0 m/s, and we can use the time calculated to find out how far the ball falls solely under gravity. The vertical distance y can be found using the formula for displacement under constant acceleration:
y = 0.5 * g * t^2, where g is the acceleration due to gravity (9.8 m/s^2)
y = 0.5 * 9.8 m/s^2 * (0.701 s)^2 ≈ 2.41 m
Therefore, the height of the tennis ball from the court when it leaves the racket is approximately 2.41 meters.