To determine the maximum height reached by the ball, we can use one of the kinematic equations that relates initial velocity, acceleration, and displacement. The equation we use is:
[tex]\[ v^2 = u^2 - 2gh \][/tex]
where:
- [tex]\( v \)[/tex] is the final velocity (0 m/s at the maximum height),
- [tex]\( u \)[/tex] is the initial velocity (13 m/s),
- [tex]\( g \)[/tex] is the acceleration due to gravity (9.8 m/s²),
- [tex]\( h \)[/tex] is the maximum height.
Since at the maximum height the final velocity [tex]\( v \)[/tex] is 0, we can rearrange the equation to solve for [tex]\( h \)[/tex]:
[tex]\[ 0 = u^2 - 2gh \][/tex]
Rearranging gives us:
[tex]\[ h = \frac{u^2}{2g} \][/tex]
Now we plug in the given values:
- [tex]\( u = 13 \)[/tex] m/s
- [tex]\( g = 9.8 \)[/tex] m/s²
[tex]\[ h = \frac{(13 \, \text{m/s})^2}{2 \cdot 9.8 \, \text{m/s}^2} \][/tex]
Calculating [tex]\( h \)[/tex]:
[tex]\[ h = \frac{169 \, \text{m}^2 / \text{s}^2}{19.6 \, \text{m/s}^2} \][/tex]
[tex]\[ h = 8.622448979591836 \, \text{m} \][/tex]
Thus, the maximum height reached by the ball is approximately 8.6 meters.
Therefore, the correct answer is:
C. 8.6 m
