Answer
$h=0.0667~m=6.67~cm$
Work Step by Step
Let the positive direction be upward with origin at the ground.
- First weight: $x_{0_1}=h$, $x_1=0$, $v_{0_1}=0$, $a=-g=-9.81~m/s^2$, $t_1=t$
$x_1=x_{0_1}+v_{0_1}t_1+\frac{1}{2}at_1^2$
$0=h+0t+\frac{1}{2}(-9.81~m/s^2)t^2$
$(4.905~m/s^2)t^2=h$
$t^2=\frac{h}{4.905~m/s^2}$ (equation 1)
- Second weight: $x_{0_2}=h+20.0~cm=h+0.200~m$, $x_2=0$, $v_{0_2}=0$, $a=-g=-9.81~m/s^2$, $t_2=t+t=2t$
$x_2=x_{0_2}+v_{0_2}t_2+\frac{1}{2}at_2^2$
$0=(h+0.200~m)+0(2t)+\frac{1}{2}(-9.81~m/s^2)(2t)^2$
$(19.62~m/s^2)t^2=h+0.200~m$
$t^2=\frac{h+0.200~m}{19.62~m/s^2}$ (equation 2)
Eliminating $t$: use equation 1 and equation 2:
$\frac{h+0.200~m}{19.62~m/s^2}=\frac{h}{4.905~m/s^2}$
$h+0.200~m=\frac{19.62~m/s^2}{4.905~m/s^2}h$
$h+0.200~m=4h$
$0.200~m=3h$
$h=\frac{0.200~m}{3}=0.0667~m=6.67~cm$
