From what height would I need to jump to fall exactly one second ?
Details and assumptions:
The initial velocity is v 0 = 0
g = 1 0 m/s 2
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What is S ?
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For this question this means height
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Then it should be mentioned.
The general formula for the distance traveled in the time t by an accelerated object is y = v o t + 2 1 a t 2 . Here v o = 0 since you simply jump from rest, and the acceleration is a = g = 1 0 . Hence, we have y = 2 1 g t 2 . So
y = 2 1 ( 1 0 ) ( 1 2 ) = 5
t = g 2 h = 1 s ⇒ h = 5 m .
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S=height
S = 2 1 ⋅ g ⋅ t 2
S = 2 1 ⋅ 1 0 ⋅ 1 2
S = 5