## Fundamentals of Physics Extended (10th Edition)

$t=[\sqrt {v^{2}_{0}+2gh}-v_{0}]/g$
We know the following equation: $v_{f}=v_{0}+gt$ We substitute the answer from part a: ($v_{f}=\sqrt {v^{2}_{0}+2gh}$): $\sqrt {v^{2}_{0}+2gh}=v_{0}+gt$ We subtract $v_{0}$ from both sides: $\sqrt {v^{2}_{0}+2gh}-v_{0}=gt$ Finally, we divide both sides by $g$: $t=[\sqrt {v^{2}_{0}+2gh}-v_{0}]/g$