Question

How long does it take for a rock to fall 90m if dropped from rest?

Answer 1

\[\ddot y=\vec a_y=-g\]\[\dot y=\vec v_y=\int\limits_0^t-g\mathrm dt'=-gt+{v_y}_o\]\[y=\int\limits_0^T(-gt+{v_y}_o)\mathrm dt=\frac{-gT^2}2+{v_y}_oT+y_o\]
\[y-y_o=\frac{-gT^2}2+{v_y}_oT\]
dropped from rest \(\implies {v_y}_o=0\)

\[y_o-y=\frac{gT^2}2\]
\[\sqrt{\frac{2(y_o-y)}g}=T\]

\(y_o-y\) is the hight fallen

Answer 2

\[3\sqrt{2} \] seconds?

Answer 3

\[s=\frac{ 1 }{ 2 }*g*t^2\] \[\frac{ 1 }{ 2 }* 10*t^2=90\] so\[t=3\sqrt{2}\] ??