Question 211164
You are trying to find the time, t, at which the height, h, of the object is zero (initial height) again. I say again because it starts out at h = 0.
So you set h = 0 and solve for t.
{{{-16t^2+104t = 0}}} Factor t from the left side.
{{{t(-16t+104) = 0}}} So...
{{{t = 0}}} (Initial condition) or:
{{{-16t+104 = 0}}} and...
{{{-16t = -104}}} Divide both sides by -16.
{{{t = 6.5}}}seconds.
The oject returns to its point of departure in 6.5 seonds.