If you drop a stone from a rooftop and hear its impact on the ground after 2 seconds, how far did it fall in meters, if its initial speed at release was zero? (Use g = 10 (m/s^2))

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cryssatemp cryssatemp · Answer 1 · 2020-02-09T03:08:22+01:00

Answer: 20 meters

Explanation:

This situation is related to vertical motion, especifically an object in free fall, and the parametric equation that describes this motion is:

[tex]y=y_{o}+V_{o}t-\frac{g}{2}t^{2}[/tex]

Where:

[tex]y= 0 m[/tex] is the stone's final height

[tex]y_{o}[/tex] is the stone's initial height

[tex]V_{o}=0 m/s[/tex] is the initial speed of the stone

[tex]t=2 s[/tex] is the time the stone is falling

[tex]g=10 m/s^{2}[/tex] is the acceleration due gravity

Isolating [tex]y_{o}[/tex] according to the given information:

[tex]y_{o}=\frac{g}{2}t^{2}[/tex]

[tex]y_{o}=\frac{10 m/s^{2}}{2}(2 s)^{2}[/tex]

Finally:

[tex]y_{o}=20 m[/tex] This is the distance the stone fell