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Answered

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A thermometer falls from a weather
balloon at a height of 7,744 ft. If the
equation for height as a function of time
is h(t) = -16t2 + initial height wheret is
time in seconds and h(t) is height in feet,
how many seconds will it take for the
thermometer to hit the ground?
[?] seconds

Sagot :

Answer:

It will take 22 seconds for the thermometer to hit the ground.

Step-by-step explanation:

A thermometer falls from a weather balloon at a height of 7,744 ft.

This means that the initial height is of 7744ft.

h(t) = -16t2 + initial height

So

[tex]h(t) = -16t^2 + 7744[/tex]

How many seconds will it take for the thermometer to hit the ground?

This is t for which [tex]h(t) = 0[/tex]. So

[tex]0 = -16t^2 + 7744[/tex]

[tex]16t^2 = 0 + 7744[/tex]

[tex]t^2 = \frac{7744}{16}[/tex]

[tex]t = \sqrt{\frac{7744}{16}}[/tex]

[tex]t = 22[/tex]

It will take 22 seconds for the thermometer to hit the ground.

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