You drop a rock down a well that is 5.4 m deep. How long does it take for the rock to hit the bottom of the well?
Answer (3)
Equation of motion:
y f = y o + v o t + 2 1 a t 2
Since initial velocity is zero, the second term goes away:
y f = y o + 0 + 2 1 a t 2
y f = y o + 2 1 a t 2
y f − y o = 2 1 a t 2
y f − y o = 5.4 m
5.4 m = 2 1 a t 2
a 2 ( 5.4 m ) = t 2
a = g = 9.81 s 2 m
9.81 s 2 m 2 ( 5.4 m ) = t 2
1.1 s 2 = t 2 1.1 s 2 = t 2
t = 1.05 s
1.05 s ;
The rock takes approximately 1.05 seconds to hit the bottom of a 5.4-meter deep well when dropped. This calculation uses the equations of motion under gravity. We found this by solving for time using the distance and acceleration due to gravity.
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