Question

If an average-sized man with a parachute jumps from an airplane, he will fall 12.5(0.2t − 1) + 19t feet in t seconds. How long will it take him to fall 142 feet? (Round your answer to two decimal places.)

Answer 1

Hi. Is the (.2t-1) supposed to be squared anywhere due to acceleration being rated with respect to time squared...? If not, all you have to do is create an equation:

`142=12.5(.2t-1)+19t`

Then, you factor out all those parts within the parenthesis to that 12.5, giving you:


`142=2.5t-12.5+19t=21.5t-12.5`

Move all non-t values to the numerical side:


`142+12.5=21.5t`

divide both sides by the coefficient of the variable t, and that will be your time, 7.186

Answer 2

It will take
`7.19s` to fall
`142ft`

Explanation:

We have the data of the function that represents the falling. Let's call this function ''f''. The function ''f'' depends of the time variable ''t''. We can write the function as :

`f(t)=12.5(0.2t-1)+19t`

In the function, if we replace the variable ''t'' by any value in seconds it will return the value in feets of how much the average-sized man has fallen for that value of ''t''.

In order to find how long it will take him to fall
`142ft`, we need to replace
`f(t)` by 142 and find the value of ''t'' that satisfies the equation.

Working with the function :

`142=12.5(0.2t-1)+19t`

`142=2.5t-12.5+19t`

`154.5=21.5t`

`t=(154.5)/(21.5)`

`t=7.1860` ≅
`7.19s`

We can't forget in the last step that the unit for time in the function is seconds.

The correct answer is
`7.19s`