the solutions just say "use v^2 = u^2 + 2as" and then give the value of 7.1m. However isnt the answer supposed to be closer to 8.1 after accounting for the the initial height (it wasn't thrown from the ground)
Yeah it's wrong. According to my calculator, even if you ignore adding the 0.8m, the height of the ball (above the line thing) is 7.3m to 1 decimal place. Nice rounding!