Question 706509
h(t)=-16t^2-62t + 188
when the marble hits the ground, the height is 0.  Set h(t) to 0 and solve for t:
0=-16t^2-62t + 188
0=16t^2+62t-188
0=8t^2+31t-94
0=8t^2-16t+47t-94
0=(8t^2-16t)+(47t-94)
0=8t(t-2)+47(t-2)
0=(t-2)(8t+47)
t = {-47/8, 2}
throw out the negative value (extraneous) leaving:
t = 2 seconds