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.I
distance= Vinitial*time+ 1/2 a*time^2
Memorize that formula. It is pretty basic
To determine the distance the basketball player runs, we can use the equation of motion:
\[v = u + at\]
where:
- \(v\) is the final velocity (6.2 m/s)
- \(u\) is the initial velocity (0 m/s since the player starts from rest)
- \(a\) is the acceleration (which we need to find)
- \(t\) is the time taken (1.9 s)
Rearranging the equation to solve for acceleration, we have:
\[a = \frac{v - u}{t}\]
Substituting the given values, we get:
\[a = \frac{6.2 \, \text{m/s} - 0 \, \text{m/s}}{1.9 \, \text{s}}\]
Simplifying the equation, we find that the acceleration of the player is:
\[a = \frac{6.2 \, \text{m/s}}{1.9 \, \text{s}} \approx 3.26 \, \text{m/s}^2\]
Now, we can use the equation of motion again to find the distance traveled:
\[s = ut + \frac{1}{2}at^2\]
Substituting the known values, we get:
\[s = 0 \, \text{m/s} \times 1.9 \, \text{s} + \frac{1}{2} \times 3.26 \, \text{m/s}^2 \times (1.9 \, \text{s})^2\]
Simplifying the equation, we find that the distance the player runs is:
\[s \approx 5.88 \, \text{m}\]
Therefore, the basketball player runs approximately 5.88 meters before slamming dunking the ball.