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

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

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 = (7744)/(16)`

`t = \sqrt{(7744)/(16)}`

`t = 22`

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