1010 Time to wait in dropping a stone | Rectilinear Translation

$h_1 = v_{i1}t - \frac{1}{2}gt^2$

$600 - 200 = 300t - \frac{1}{2}(32.2)t^2$

$16.1t^2 - 300t + 400 = 0$

$t = 17.19 \, \text{ sec and } \, 1.44 \, \text{ sec}$

With t = 17.19 sec
$200 = \frac{1}{2}(32.2)(17.19 - t_2)^2$

$t_2 = 13.67 \, \text{ sec}$
 

With t = 1.44 sec
$200 = \frac{1}{2}(32.2)(1.44 - t_2)^2$

$t_2 = -2.08 \, \text{ sec}$   (meaningless)
 

Use $t_2 = 13.67 \, \text{ sec}$           answer

$h_1 = v_{i1}t - \frac{1}{2}gt^2$

$182.88 - 60.96 = 91.44t - \frac{1}{2}(9.81)t^2$

$4.905t^2 - 91.44t + 121.92 = 0$

$t = 17.19 \, \text{ sec and } \, 1.44 \, \text{ sec}$

With t = 17.19 sec
$60.96 = \frac{1}{2}(9.81)(17.19 - t_2)^2$

$t_2 = 13.67 \, \text{ sec}$
 

With t = 1.44 sec
$60.96 = \frac{1}{2}(32.2)(1.44 - t_2)^2$

$t_2 = -2.08 \, \text{ sec}$   (meaningless)
 

Use $t_2 = 13.67 \, \text{ sec}$           answer