SOLUTION: Please help me to solve this problem= 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

Question 234948: Please help me to solve this problem=
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?
Thank you for helping me to solve this problem.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?
:
Using gravity expression for falling objects: h = 16t^2,
where
t = time in sec
h = height in ft
:
Hal's rock in the air 3 sec less than Stu's
Stu's height is 4 time Hal's height
:
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
;
:
Check solution by multiplying Hal's height by 4
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