The plot of $c(t)=(x(t),y(t))$ is Figure (III).
Work Step by Step
The graph of $x(t)$ goes up as $t$ increases, while $y(t)$ goes up and reaches a maximum point and then goes down to 0. In Figure (I) both $x$ and $y$ increases. In Figure II, $x$ increases but then decreases to 0; and $y$ never reaches 0. In Figure (III), $y$ increases and reaches the maximum height and then decreases to 0, while $x$ increases and reaches a certain value when $y$ reaches 0. So, the plot of $c(t)=(x(t),y(t))$ is Figure (III).