Question 22186
The general form of the equation for the height of an object propelled upward with an initial velocity of v{{{0}}} from an initial height of h{{{0)}}} is {{{h(t) = -16t^2 + v0t + h0}}}, and since the depth of the canyon by which Jacob is standing is really irrelevant, your initial equation is correct. The initial height is zero feet.
{{{h(t) = -16t^2 + 32t}}} 
Now you would like to find out at what time (t) will the ball return to its initial height of 0 ft.

Setting h(t) = 0 ft. you can write:
{{{-16t^2 + 32t = 0}}} Solve for t by factoring -16t from both sides.
{{{-16t(t - 2) = 0}}} Apply the zero product principle.
{{{t - 2 = 0}}} Add 2 to both sides.
{{{t = 2}}}

The ball will return to its initial height of 0 ft. in 2 seconds.

Check: Set t = 2
{{{h(2) = -16(2^2) + 32(2)}}} Solve for h.
{{{h(2) = -64 + 64}}}
{{{h(2) = 0}}} ft.