SOLUTION: I am stuck on this word problem would you be able to help me work it out? A ball is thrown upward from the roof of a building 100 m tall with an initial velocity of 20 m/s. W

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Question 104025: I am stuck on this word problem would you be able to help me work it out?
A ball is thrown upward from the roof of a building 100 m tall with an initial velocity of 20 m/s. When will the ball reach a height of 80 m?
This problem has me confused I am not sure where to begin. Thanks for your help.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A ball is thrown upward from the roof of a building 100 m tall with an initial velocity of 20 m/s. When will the ball reach a height of 80 m?
:
This can be made into a quadratic equation with the three elements
Let t = time in seconds
1. Gravity (negative because it's accelerated downward) -4.9t^2
2. Initial velocity (positive because it's thrown up-ward: + 20t
3. Initial height above ground: +100
:
-4.9t^2 + 20t + 100 = height above ground
:
They want to know when will it be at a height of 80 ft:
-4.9t^2 + 20t + 100 = 80
:
-4.9t^2 + 20t + 100 - 80 = 0; subtracted 80 from both sides
:
-4.9t^2 + 20t + 20 = 0
:
This is the quadratic formula: except we will be solving for t instead of x:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
Substitute: a=-4.9; b=20; c=20
t+=+%28-20+%2B-+sqrt%28+20%5E2+-+4+%2A+-4.9+%2A+20+%29%29%2F%282%2A-4.9%29+
Do the math:
t+=+%28-20+%2B-+sqrt%28400+-+%28-392%29+%29%29%2F%28-9.8%29+
t+=+%28-20+%2B-+sqrt%28400+%2B+392+%29%29%2F%28-9.8%29+; minus a minus is a plus
:
t+=+%28-20+%2B-+sqrt%28792%29%29%2F%28-9.8%29+
:
t+=+%28-20+%2B-+28.1425%29%2F%28-9.8%29+
Solution 1
t+=+%28-20+%2B28.1425%29%2F%28-9.8%29+
t+=+8.1425%2F%28-9.8%29
t = -.83, this is NOT our solution
:
Solution 2:
t+=+%28-20+-+28.1425%29%2F%28-9.8%29+
t+=+-48.1425%2F%28-9.8%29
:
t = + 4.9 sec, this IS our solution