Question

A rock falls from a tower that is 160 feet high. As it is falling, it’s height is given by the formula h=160-16t^2. How many seconds will it take for the rock to hit the ground (h=0)? Round your answer to the nearest tenth if necessary.

Answer 1

Given

$h=160-16t^2$

Where h is the height of the falling rock at time t, set h=0 and solve for t, as shown below

$\begin{gathered} 160-16t^2=0 \\ \Rightarrow16t^2=160 \\ \Rightarrow t^2=10 \\ \Rightarrow t=\pm\sqrt{10} \end{gathered}$

However, it is not possible that t<0 as it would imply that the rock reached the ground before falling; therefore, the only possible answer is t=sqrt(10).

Rounding the answer,

$\begin{gathered} \Rightarrow t=\sqrt{10} \\ \Rightarrow t\approx3.2 \end{gathered}$

Hence, the answer is t=3.2