Question

A pine cone drops from a tree branch that is 36 feet above the ground. The function h = –16t2 + 36 is used. If the height h of the pine cone is in feet after t seconds, at about what time does the pine cone hit the ground? Could 2 seconds be a reasonable answer to this model?

Answer 1

Notice that the height of the pine cone when it hits the ground is zero. So, to find the tame it takes for the pine cone to hit the ground, we just need to replace the height, $h$, with 0 in the function, and solve for time $t$:
$h=-16t^2+36$
$0=-16t^2+36$
$-36=-16t^2$
$t^2= \frac{-36}{-16}$
$t^2= \frac{9}{4}$
$t=(+/-) \sqrt{ \frac{9}{4} }$
$t=(+/-) \frac{3}{2}$
$t=(+/-)1.5$
Since time cannot be negative, the solution is $t=1.5$ seconds.

Since 1.5 second is significantly less than 2 seconds, we can conclude that 2 seconds is not a reasonable answer to this model.

Answer 2

We have that
h = –16t² + 36

using a graph tool
see the attached figure
the x-intercept is when the pine cone hit the ground
h=0 for t=1.5 sec

therefore

the answer part a) is
1.5 seconds

Part b)Could 2 seconds be a reasonable answer to this model?
h = –16t² + 36
for t=2 sec
h=-16*(2)²+36-------> h=-64+36------> h=-25 ft

the answer Part b) is
2 seconds is not a reasonable answer to this model, because the height h of the pine cone cannot be negative
the domain of the model is for the values of t included in the interval [0,1.5]