A rock thrown vertically upward from the surface of the moon at a velocity of $\displaystyle 24$ $\displaystyle \frac{m}{sec}$ reaches a height of $\displaystyle s=24t-0.8t^2$ meters in $\displaystyle t$ $\displaystyle sec$.

a. Find the rock's velocity and acceleration at time $\displaystyle t$ $\displaystyle \rightarrow v=24-1.6t$ $\displaystyle \frac{m}{s}$ $\displaystyle a=-1.6$ $\displaystyle \frac{m}{s^2}$

b. How long does it take the rock to reach its highest point? $\displaystyle \rightarrow 24-1.6t=0$ $\displaystyle t=15$ $\displaystyle sec$

c. How high does the rock go? $\displaystyle \rightarrow s_{max}=24(15)-0.8(15)^2$ $\displaystyle s_{max}=180$ $\displaystyle m$

d. How long does it take the rock to reach half its maximum height?

e. How long is the rock aloft? $\displaystyle \rightarrow 30$ $\displaystyle sec$

I don't know how to find how long it takes the rock to reach half its max height. How would I solve this?