In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints to a speed of 7.30 m/s in 1.26s. Assuming that player accelerates uniformly, determine the distance he runs.
We can use the equation:
\[v = u + at\]
where
\(v = 7.30 \, \text{m/s}\) (final velocity),
\(u = 0 \, \text{m/s}\) (initial velocity),
\(a = ?\) (acceleration), and
\(t = 1.26 \, \text{s}\) (time).
Substituting the given values, we get:
\[7.30 = 0 + a \cdot 1.26\]
Simplifying this equation, we have:
\[7.30 = 1.26a\]
Dividing both sides by 1.26, we find:
\[a = \frac{7.30}{1.26} \approx 5.7937 \, \text{m/s}^2\]
To find the distance traveled, we can use the equation:
\[s = ut + \frac{1}{2} a t^2\]
where
\(s = ?\) (distance),
\(u = 0\) (initial velocity),
\(a = 5.7937 \, \text{m/s}^2\) (acceleration), and
\(t = 1.26 \, \text{s}\) (time).
Substituting the given values, we get:
\[s = 0 \cdot 1.26 + \frac{1}{2} (5.7937) (1.26)^2\]
Simplifying this equation, we find:
\[s \approx 4.5887 \, \text{m}\]
Therefore, the player runs approximately 4.5887 meters before slam-dunking the ball.