Question 1124050
<font color="black" face="times" size="3">
The starting height is h0 = 288
We want to find the value of t when h = 0, which is when the object hits the ground 


h = -16t^2 + h0
h = -16t^2 + 288 <--- replace h0 with the starting height
0 = -16t^2 + 288 <--- replace h with 0
16t^2 = 288
t^2 = 288/16
t^2 = 18
t = sqrt(18) <---- we'll only focus on positive t values
<font color=red>t = 3*sqrt(2)</font> <--- this is the exact solution
<font color=red>t = 4.2426</font> <--- this is the approximate solution


It takes about 4.2426 seconds for the object to hit the ground. Keep in mind that we are not considering air resistance at all. If the object is light enough (eg: like a feather), then air resistance will play a bigger role here. However, I'm assuming the object dropped is one such that its weight and surface area don't contribute too much that air resistance plays that much of a role.

</font>