An object is tossing upwards with an initial speed of $64 \text{ feet/sec}$.Suppose the gravitational acceleration is $32\text{ feet/sec}^2$. Find the smallest $t$ such that the object reaches the height of $96\text{ feet}$ at time $t$.
My problem: Which formula I have to use to find $t$?
Thanks.
We have $$ s = ut + \frac{1}{2}at^2 $$
which we can rearrange to get $$ t^2 + 2 \dfrac{2u}{a} - 2 \dfrac{s}{a} = 0 $$ and applying the quadratic equation to that (with correct values of s, u, and a) should get you your answer!