Question

I need help with question

Answer 1

Check the picture below.

so the ball hits the ground when g(x) = 0

`\stackrel{g(x)}{0}=-16t^2+30t\implies 0=-2t(8t-15) \\\\[-0.35em] ~\dotfill\\\\ 0=-2t\implies \boxed{0=t} \\\\[-0.35em] ~\dotfill\\\\ 0=8t-15\implies 15=8t\implies \cfrac{15}{8}=t\implies \stackrel{ seconds }{\boxed{1.9\approx t}}\qquad \textit{falls to the ground}`

we get two values for "t", once at 0, because that's when the ball was at rest before being kicked.