In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints to a speed of 11.1 m/s in 2.30 s. Assuming that the player accelerates uniformly, determine the distance he runs.

To determine the distance the basketball player runs, we can use the formula:

distance = initial velocity * time + (1/2) * acceleration * time^2

In this case, the basketball player starts from rest, so the initial velocity (u) is 0 m/s. The final velocity (v) is 11.1 m/s, and the time (t) is 2.30 s.

Since the player accelerates uniformly, we can determine the acceleration (a) using the equation:

acceleration = (final velocity - initial velocity) / time

Substituting the given values, we have:

acceleration = (11.1 m/s - 0 m/s) / 2.30 s

Simplifying the equation, we find:

acceleration = 11.1 m/s / 2.30 s
acceleration = 4.826 m/s^2 (rounded to three decimal places)

Now, we can substitute the values of initial velocity, time, and acceleration into the distance formula:

distance = initial velocity * time + (1/2) * acceleration * time^2
distance = 0 m/s * 2.30 s + (1/2) * 4.826 m/s^2 * (2.30 s)^2

Simplifying further:

distance = 0 m + (1/2) * 4.826 m/s^2 * 5.29 s^2
distance = 0 m + 11.28 m

Therefore, the distance the basketball player runs is approximately 11.28 meters.