Answer:
After 10 seconds
Step-by-step explanation:
In this problem, the height of the object after t seconds is described by the function
where
160 ft is the initial height of the object at t = 0
+144 ft/s is the initial velocity
is the acceleration due to gravity (downward)
Here we want to find the time at which the object hits the ground, so the time t at which
Therefore we can write
Simplifying (dividing each term by 16), we get
This is a second-order equation in the form
Which has solutions given by the formula
(2)
Here we have:
a = -1
b = 9
c = 10
Substituting into (2) we find the solutions:
Which gives:
Since time cannot be negative, the only solution is
t = 10 seconds