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

Answer:

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

Step-by-step 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 :

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

$142=2.5t-12.5+19t$

$154.5=21.5t$

$t=\frac{154.5}{21.5}$

$t=7.1860$ ≅ $7.19s$

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

The correct answer is $7.19s$