Determine the velocity of the ball after $t$ seconds which is launched straight up from the top of a building with an initial speed of $40\text{ ft/s}$ from a height of $60\text{ ft}$ above the ground. The height (in feet) of the ball above the ground $t$ seconds after it is launched is given by the equation $h\left(t\right)=-16t^2+40t+60$.

The position of a cyclist moving in a straight line is described by the function $p\left(t\right)=20t-5t^2$, where $p$ is in kilometers and $t$ is in hours. Find the intervals where the cyclist's speed is increasing for $0\le t\le 5$.

A diver jumps off a diving board $10$ feet above the pool with an initial upward velocity of $16\text{ ft/s}$. The height (in feet) of the diver above the water $t$ seconds after the jump is given by $s\left(t\right)=-16t^2+16t+10$. What is the maximum height of the diver above the water?