SOLUTION: A rock is thrown vertically upward with a speed of 15.0 m/s from the roof of a building that is 70.0 m above the ground. Assume free fall. What is the speed of the rock just before

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Question 1144619: A rock is thrown vertically upward with a speed of 15.0 m/s from the roof of a building that is 70.0 m above the ground. Assume free fall. What is the speed of the rock just before it strikes the ground?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A rock is thrown vertically upward with a speed of 15.0 m/s from the roof of a building that is 70.0 m above the ground. Assume free fall. What is the speed of the rock just before it strikes the ground?
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Using 10 m/sec/sec for Earth's gravity:
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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
Find the time until impact, when h(t) = 0
-5t^2 - 15t = 0
t = 0 (Ignore)
t = 3 seconds (from the time the rock passes roof descending)
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v = 15 m/sec + 3*10 m/sec = 45 m/sec at impact
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Ikelyn spotted my error, and here is hers:
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t%5B1%2C2%5D = %28-3+%2B-+sqrt%283%5E2+%2B+4%2A14%29%29%2F2 = %28-3+%2B-+sqrt%28177%29%29%2F2.

Only positive root is meaningful t = %28-3+%2B+sqrt%28177%29%29%2F2 = 2.531 seconds.
======================
3%5E2+%2B+4%2A14+=+65 not 177
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We all say at some time, "That was a stupid mistake."
You never hear, "That's a mistake I'm proud of."

Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.

            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.


  t%5B1%2C2%5D = %28-3+%2B-+sqrt%283%5E2+%2B+4%2A14%29%29%2F2 = %28-3+%2B-+sqrt%2865%29%29%2F2.


Only positive root is meaningful  t = %28-3+%2B+sqrt%2865%29%29%2F2 = 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


/\/\/\/\/\/\/\/

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  (!)