Conversion of Translational Motion Forumula

[TrueBlood]

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I am unable to see how time = [Vo][SQRT(2[Change in x]/g)], as written in the answer #7 for BR Physics passage 1, section 1.

Using [Change in X] = Vo[Change in Time] + 1/2g[change in time]^2

[Change in X] - Vo[Chaneg in Time] = 1/2g[change in time]^2

2[Change in X] - 2Vo[Change in Time] = g[change in time]^2

2[Change in X]/g - 2Vo[Change in Time]/g = [change in time]^2

SQRT(2[Change in X]/g) - SQRT(2Vo[Change in Time]/g) = time



So essentially, I quickly realized how they found time = SQRT(2[Change in X]/g), when you only care about height and gravity, but can't get time = [Vo][SQRT(2[Change in x]/g)] when you need to consider the original velocity.

Thanks