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
\(h(t) = - 16t^2 + \text{initial height}\)
where
t = instantaneous time during drop (in seconds)
h = instantaneous height during drop(in feet)
Initial height is given as 7744 feet
Equation:
\(h(t) = -16t^2 + 7744\)
When the thermometer ultimately hits the ground the height will be 0 giving us this equation
\(0 = -16t^2 + 7744\\\\\)
Move \(-16t^2\) to the left side:
\(16t^2 = 7744\)
Divide both sides by 16:
\(t^2 = 7744/16 = 484\)
\(t = \pm \sqrt{484}\)
\(t = \pm 22\)
We can ignore the negative value and therefore
t = 22 seconds
