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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.)

Respuesta :

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:
[tex]142=12.5(.2t-1)+19t[/tex]

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

[tex]142=2.5t-12.5+19t=21.5t-12.5[/tex]

Move all non-t values to the numerical side:

[tex]142+12.5=21.5t[/tex]

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

Answer:

It will take [tex]7.19s[/tex] to fall [tex]142ft[/tex]

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 :

[tex]f(t)=12.5(0.2t-1)+19t[/tex]

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 [tex]142ft[/tex], we need to replace [tex]f(t)[/tex] by 142 and find the value of ''t'' that satisfies the equation.

Working with the function :

[tex]142=12.5(0.2t-1)+19t[/tex]

[tex]142=2.5t-12.5+19t[/tex]

[tex]154.5=21.5t[/tex]

[tex]t=\frac{154.5}{21.5}[/tex]

[tex]t=7.1860[/tex] ≅ [tex]7.19s[/tex]

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

The correct answer is [tex]7.19s[/tex]

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