Understanding the Concepts

* Displacement: The overall change in position from the starting point.

* Maximum Height: The highest point the ball reaches before falling back down.

* Gravity: Acts downward on the ball, slowing it down as it goes up and speeding it up as it comes down.

Calculations

1. Find the time it takes to reach maximum height:

* At the maximum height, the ball's velocity is 0. We can use the following kinematic equation:

* v_f = v_i + at

* where:

* v_f = final velocity (0 m/s)

* v_i = initial velocity (4 m/s)

* a = acceleration due to gravity (-9.8 m/s²)

* t = time

* Solving for t:

* 0 = 4 + (-9.8)t

* t = 4 / 9.8 ≈ 0.41 seconds

2. Find the maximum height (displacement):

* Use another kinematic equation:

* Δy = v_i*t + (1/2)at²

* where:

* Δy = displacement (maximum height)

* Plugging in the values:

* Δy = (4 m/s)(0.41 s) + (1/2)(-9.8 m/s²)(0.41 s)²

* Δy ≈ 0.82 m

Answer:

The maximum displacement of the tennis ball is approximately 0.82 meters.