Byron S. answered • 11/03/14

Math and Science Tutor with an Engineering Background

I believe your formula should have a negative on t

^{2}term:s = (-1/2)gt

^{2 }+ v_{0}t + s_{0}To find any extreme value, you'll take the first derivative, set it equal to zero and solve. g, v0, and s0 are constants, so treat them like numbers, not variables.

s' = (-1/2)g(2t) + v

_{0}s' = -gt + v

_{0}= 0The critical value is t = v

_{0}/gYou can then plug this into the original equation to solve for the maximum height.

s

_{max}= (-1/2)g(v_{0}/g)^{2}+ v_{0}(v_{0}/g) + s0s

_{max}= - v_{0}/(2g) + v_{0}^{2}/g + s_{0}You can combine by using a common denominator of 2g if you like.