Question

A falling object travels a distance given by the formula d= 2t + 4t², where d is measured in feet and t is measured inseconds. How many seconds will it take for the object to travel 71 feet? Round the answer to 4 decimal places.secondshelp (numbers)

Answer 1

`3.9705\text{ seconds}`

Step-by-step explanation

To find how many seconds it will take to travel 71 feet, substitute the value of d to be 71 feet and solve for t in the equation:

`\begin{gathered} 71=2t+4t^2 \\ \Rightarrow4t^2+2t-71=0 \end{gathered}`

Solve for t using the Quadratic formula:

`a=4,b=2,c=-71`

Therefore, we have:

`\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t=\frac{-2\pm\sqrt[]{2^2-(4\cdot4\cdot-71)}}{2\cdot4} \\ t=\frac{-2\pm\sqrt[]{4+1136}}{8}=\frac{-2\pm\sqrt[]{1140}}{8} \\ \Rightarrow t=(-2+33.7639)/(8);t=(-2-33.7639)/(8) \end{gathered}`

Since time cannot be negative, we only use the first value:

`\begin{gathered} t=(-2+33.7639)/(8)=(31.7639)/(8) \\ t=3.9705\text{ seconds} \end{gathered}`

That is the time it will take.