Answer :
Answer:
The length of the incline is 3.504 meters.
Explanation:
Let suppose that Julietta's ball decelerates uniformly, then we determine the length of the incline is determined by the following equation of motion:
[tex]\Delta s = v_{o}\cdot t +\frac{1}{2}\cdot a \cdot t^{2}[/tex] (Eq. 1)
Where:
[tex]\Delta s[/tex] - Length of the incline, measured in meters.
[tex]v_{o}[/tex] - Initial speed of the ball, measured in meters per second.
[tex]a[/tex] - Aceleration of the ball, measured in meters per square second.
[tex]t[/tex] - Time, measured in second.
If we know that [tex]v_{o} = 2.95\,\frac{m}{s}[/tex], [tex]t = 1.54\,s[/tex] and [tex]a = -0.876\,\frac{m}{s^{2}}[/tex], then the length of the incline is:
[tex]\Delta s = \left(2.95\,\frac{m}{s} \right)\cdot (1.54\,s)+\frac{1}{2}\cdot \left(-0.876\,\frac{m}{s^{2}} \right) \cdot (1.54\,s)^{2}[/tex]
[tex]\Delta s = 3.504\,m[/tex]
The length of the incline is 3.504 meters.