Answer: At
, the pebble hit the top of the boulder.
Step-by-step explanation:
Since we have given that
Distance at which Selena is standing on a rock cliff = 52 feet
Height of boulder above a rock cliff = 12 foot
So, the given quadratic equation would be
![p(t)=-16t^2+12t+52](https://tex.z-dn.net/?f=p%28t%29%3D-16t%5E2%2B12t%2B52)
First we derivative it w.r.t t,
![p'(t)=-32t+12](https://tex.z-dn.net/?f=p%27%28t%29%3D-32t%2B12)
Now, we will find the critical value,
![-32t+12=0\\\\-32t=-12\\\\t=\dfrac{12}{32}=\dfrac{6}{16}=\dfrac{3}{8}](https://tex.z-dn.net/?f=-32t%2B12%3D0%5C%5C%5C%5C-32t%3D-12%5C%5C%5C%5Ct%3D%5Cdfrac%7B12%7D%7B32%7D%3D%5Cdfrac%7B6%7D%7B16%7D%3D%5Cdfrac%7B3%7D%7B8%7D)
Now, we will check whether it is maximum or not.
![p''(t)=-32](https://tex.z-dn.net/?f=p%27%27%28t%29%3D-32%3C0)
So, we get that it is maximum.
Hence, at
, the pebble hit the top of the boulder.