The object will reach the ground after 5 seconds.
The height of the object after t seconds can be found using the equation:
h(t) = -16t^2 + 171t + 7
where h(t) is the height in feet and t is the time in seconds.
To find when the object reaches the ground, we need to find when h(t)=0. We can do this by setting h(t)=0 and using the quadratic formula to solve for t.
h(t) = 0
-16t^2 + 171t + 7 = 0
t = (-171 ± √(171^2 - 4 * -16 * 7)) / (2 * -16)
t = (5 ± √(2789)) / -32
t = (5 ± 53.8) / -32
t = -5.3, 5
We can ignore the negative solution, since time cannot be negative. Therefore, the object will reach the ground after 5 seconds.