6.07 m
Explanation:
Given:
[tex]v_0=24.5\:\text{m/s}[/tex]
[tex]\theta_0 = 35.5°[/tex]
First, we need to find the amount of time it takes to travel a horizontal distance of 25.8 m. We know that
[tex]x = v_{0x}t \Rightarrow t = \dfrac{x}{v_0 \cos \theta_0}[/tex]
or
[tex]t = 1.29\:\text{s}[/tex]
To find the vertical height where the ball hit the wall, we use
[tex]y = v_{0y}t - \frac{1}{2}gt^2[/tex]
[tex]\:\:\:\:=(24.5\:\text{m/s})\sin 35.5(1.29\:\text{s}) \\ - \frac{1}{2}(9.8\:\text{m/s}^2)(1.29\:\text{s})^2[/tex]
[tex]\:\:\:\:=6.07\:\text{m}[/tex]
