A stone is thrown from a rooftop at time $t = 0$ seconds. Its position at time $t$ is given by $\vec{r}(t) = 8t\boldsymbol{i}-5t\boldsymbol{j}+\left(9.8-4.9t^{2}\right)\boldsymbol{k}.$ The origin is at the base of the building, which is standing on flat ground. Distance is measured in meters. The vector $\boldsymbol{i}$ points east, $\boldsymbol{j}$ points north, and $\boldsymbol{k}$ points up.

(a) How high is the rooftop? meters.

(b) When does the stone hit the ground? seconds.

(c) Where does the stone hit the ground? (in meters)

(d) How fast is the stone moving when it hits the ground? (in meters per second)