Question

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

Answer 1

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

$h(t) = -16t^2 + 7744$

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

This is t for which $h(t) = 0$. So

$0 = -16t^2 + 7744$

$16t^2 = 0 + 7744$

$t^2 = \frac{7744}{16}$

$t = \sqrt{\frac{7744}{16}}$

$t = 22$

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