1008 Stones thrown vertically upward | Rectilinear Translation

$s = v_it + \frac{1}{2}at^2$

$h = v_it - \frac{1}{2}gt^2$

$h = v_it - \frac{1}{2}(32.2)t^2$

$h = v_it - 16.1t^2$
 

For the first stone:
$h_1 = 48.3t - 16.1t^2$
 

For the second stone
$h_2 = 96.6(t - 1) - 16.1(t - 1)^2$

$h_2 = 96.6(t - 1) - 16.1(t^2 - 2t + 1)$

$h_2 = 96.6t - 96.6 - 16.1t^2 + 32.2t - 16.1$

$h_2 = -16.1t^2 + 128.8t - 112.7$
 

$h_1 = h_2$

$48.3t - 16.1t^2 = -16.1t^2 + 128.8t - 112.7$

$80.5t = 112.7$

$t = 1.4 \, \text{ s}$
 

$h = 48.3(1.4) - 16.1(1.4^2)$

$h = 36.064 \, \text{ ft}$           answer

$s = v_it + \frac{1}{2}at^2$

$h = v_it - \frac{1}{2}gt^2$

$h = v_it - \frac{1}{2}(9.81)t^2$

$h = v_it - 4.905t^2$
 

For the first stone:
$h_1 = 14.72t - 4.905t^2$
 

For the second stone
$h_2 = 29.44(t - 1) - 4.905(t - 1)^2$

$h_2 = 29.44(t - 1) - 4.905(t^2 - 2t + 1)$

$h_2 = 29.44t - 29.44 - 4.905t^2 + 9.81t - 4.905$

$h_2 = -4.905t^2 + 39.25t - 34.345$
 

$h_1 = h_2$

$14.72t - 4.905t^2 = -4.905t^2 + 39.25t - 34.345$

$24.53t = 34.345$

$t = 1.4 \, \text{ s}$
 

$h_1 = 14.72(1.4) - 4.905(1.4^2)$

$h = 10.994 \, \text{ m}$           answer