A thermometer falls down from a weather balloon at a height of 7,744 ft. If the equation for height as a function of time is h(t) = -16t^2 + initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the thermometer to hit the ground?



Answer :

Answer:

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

t = 22 seconds

Step-by-step explanation:

The equation for height as the thermometer falls is given by

[tex]h(t) = - 16t^2 + \text{initial height}[/tex]

where
t = instantaneous time during drop (in seconds)
h = instantaneous height during drop(in feet)

Initial height is given as 7744 feet

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

When the thermometer ultimately hits the ground the height will be 0 giving us this equation

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

Move [tex]-16t^2[/tex] to the left side:
[tex]16t^2 = 7744[/tex]

Divide both sides by 16:
[tex]t^2 = 7744/16 = 484‬[/tex]

[tex]t = \pm \sqrt{484}[/tex]

[tex]t = \pm 22[/tex]

We can ignore the negative value and therefore

t = 22 seconds