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
