Question 1034545
You want to know when the object hits the ground so I'm looking for the time when the height s = 0
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The formula is: 
s(t) = –gt^2+v_0t+h_0
The initial launch height was 58.8 meters, and the initial velocity (launch speed) was 19.6 m/s:
0 = –4.9t2+19.6t+58.8
0 = t2–4t–12
0 = (t–6)(t+2) split into 2 equations
t-6 = 0 or t+2 = 0
t = 6 or t = -2
We know the answer we are looking for is a positive number. Discard the -2:
The object strikes the ground in 6 seconds