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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
