You are hiking pine mountain and have finally reached the top. You are peering over the edge and accidentally drop your phone while taking pictures. Your phone falls and hit the ground 13 seconds later. How tall is the mountain?

The cliff is 12.71m tall.

Explanation:

Why?

Before solving the problem, we must remember that the phone was dropped, it means that there is no initial velocity, also, the acceleration acting on the phone is the acceleration due to gravity.

So, to find how tall is the cliff, we can use the following equations:

\begin{gathered}y=y_o+v_o*t-\frac{1}{2}g*t^{2}v_f=v_o+g*t\end{gathered}y=yo+vo∗t−21g∗t2vf=vo+g∗t

\begin{gathered}t=\frac{v_f}{g} t=\frac{-15.75\frac{m}{s}}{-9.81\frac{m}{s^{2}}}=1.61s\end{gathered}t=gvft=−9.81s2m−15.75sm=1.61s

Now that we know the time, we can calculate how tall is the cliff:

\begin{gathered}y=y_o+v_o*t+\frac{1}{2}g*t^{2}y=0+0*1.61s-\frac{1}{2}*(-9.81\frac{m}{s^{2}})*(1.61s)^{2}y=12.71m\end{gathered}y=yo+vo∗t+21g∗t2y=0+0∗1.61s−21∗(−9.81s2m)∗(1.61s)2y=12.71m

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