Solving Quadratic Equations by Graphing - Examples & Practice

On the fictional planet of Plutopia, the Big Bad Baseball Batter hits a ball so that its horizontal distance $x(t)$ and vertical height $y(t)$ at time $t$ (in seconds) follow the equations $$x(t) = 10t$$ and $$y(t) = -5t^2 + 50t$$ in meters. In other words, the ball has coordinates $(x(t),y(t))$ at time $t$.

Outfielder R-Hood happens to start at position $(60,0)$, on the same plane as the parabolic path of the ball. Suppose R-Hood can catch the ball as long as she is within half a meter of the ball at some time $t$.