.
Unfortunately, there is a rude mistake (a FATAL ERROR) in Alan' solution.
On the way (in his solution) he lose the height of the building.
So I came to fix it and to provide a correct solution.
Use 10 m/sec/sec for Earth's gravity.
The rock will pass the roof on its way down at the speed of 15 m/sec.
Its height at time t is h(t) = -5t^2 - 15t + 70.
Find the time until impact, when h(t) = 0 :
-5t^2 - 15t + 70 = 0
5t^2 + 15t - 70 = 0
t^2 + 3t - 14 = 0.
= = .
Only positive root is meaningful t = = 2.531 seconds.
Then the speed of the rock just before it strikes the ground is 15 + 10*2.531 = 27.656 m/s. ANSWER
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On the way, Allan noticed my typos.
Thank you, Alan !
I just fixed them, and now you see the corrected version, to which you can TRUST, finally (!)