Stu lives on the top floor of an apartment building and Hal

Stu lives on the top floor of an apartment building, and Hal lives on a lower floor. Hal\'s window is 1/4 as high as Stu\'s. Stu drops a stone from his window. Three seconds later, Hal drops a stone from his window. The two stones hit the ground simultaneously. How high is Stu\'s window from the ground?

Solution

Let t = time for Stu\'s Rock to hit the ground
:
Stu\'s ht = 4 times Hal\'s height
16t^2 = 4(16(t-3)^2)
16t^2 = 64(t-3)^2
:
Simplify. divide both sides by 16
t^2 = 4(t-3)^2
:
FOIL
t^2 = 4(t^2 - 6t + 9)
;
t^2 = 4t^2 - 24t + 36
;
Arrange as a quadratic equation on the right
0 = 4t^2 - t^2 - 24t + 36
3t^2 - 24t + 36 = 0
factor
(3t - 6)(t - 6) = 0
Two solutions
3t = 6
t = 2 sec
and
t = 6 sec, this one makes sense (Stu\'s rock\'s time to hit the ground)
:
Hal\'s time: 6 - 3 = 3 sec to hit the ground, find his height
h = 16(3^2)
h = 144 ft ft, Hal\'s height
:
Stu\'s time: 6 sec
h = 16(6^2)
h = 576 ft, Stu\'s height