In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints to a speed of 6.2 m/s in 1.9 s. Assuming that the player accelerates uniformly, determine the distance he runs.
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117.8m
To determine the distance the basketball player runs, we need to find the player's acceleration and use it to calculate the distance traveled.
First, we can find the acceleration of the basketball player using the formula:
acceleration = (final velocity - initial velocity) / time
Given that the initial velocity (vi) is 0 m/s (starting from rest), the final velocity (vf) is 6.2 m/s, and the time (t) is 1.9 s, we can substitute these values into the formula:
acceleration = (6.2 m/s - 0 m/s) / 1.9 s
acceleration = 6.2 m/s / 1.9 s
acceleration ≈ 3.26 m/s^2
Now that we know the acceleration, we can calculate the distance covered using the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Substituting the known values into the equation:
distance = (0 m/s * 1.9 s) + (0.5 * 3.26 m/s^2 * (1.9 s)^2)
distance = 0 m + (0.5 * 3.26 m/s^2 * 3.61 s^2)
distance = 0 m + (0.5 * 11.8174 m^2/s^2)
distance ≈ 5.9087 m
Therefore, the basketball player runs approximately 5.9087 meters.