Question

If the average-size man with a parachute jumps from an airplane, he will fall12.5(0.2^t– 1) + 21t feet in t seconds. How long will it take him to fall 170 feet?(Round your answers to two decimal places.)=_______sec

Answer 1

The equation relating time and fall height is given by

`h(t)=12.5(0.2^t-1)+21t`

We want to find out how long will it take him to fall 170 feet?

Let us substitute h(t) = 170

`170=12.5(0.2^t-1)+21t`

Now let's solve the equation

`\begin{gathered} 170=12.5(0.2^t-1)+21t \\ 170=2.5^t-12.5+21t \\ 170+12.5=2.5^t+21t \\ 182.5=2.5^t+21t \end{gathered}`

Taking log on both sides

`\ln (182.5)=\ln (2.5^t)+\ln (21t)_{}`