SOLUTION: A ball is thrown upward from the roof a building 100 m tall with an initial velocity of 20 m/s - when will the ball reach a height of 80 m? 80 = -16t^2 + 20t + 100 16t^2 -20t -

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A ball is thrown upward from the roof a building 100 m tall with an initial velocity of 20 m/s - when will the ball reach a height of 80 m? 80 = -16t^2 + 20t + 100 16t^2 -20t -      Log On


   

Question 90368This question is from textbook Beginning Algebra
: A ball is thrown upward from the roof a building 100 m tall with an initial velocity of 20 m/s - when will the ball reach a height of 80 m?
80 = -16t^2 + 20t + 100
16t^2 -20t -20 = 0
4t^2 - 5t - 5 = 0
t = -(-5) +/- radical (-5)^2 - 4(4)(-5) over 2(4)
t = 5 +/- radical 25 + 80 over 8
t = 5 + 10.247 over 8
t = 15.247 over 8
t = 1.906 seconds
Please confirm if I'm doing this correctly - thank you. This question is from textbook Beginning Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
80+=+-16t%5E2+%2B+20t+%2B+100 Start with the given equation

0+=+-16t%5E2+%2B+20t+%2B+20 Subtract 80 from both sides

0+=+-16t%5E2+%2B+20t+%2B+20 Subtract 80 from both sides


Let's use the quadratic formula to solve for t:


Starting with the general quadratic

at%5E2%2Bbt%2Bc=0

the general solution using the quadratic equation is:

t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve -16%2At%5E2%2B20%2At%2B20=0 ( notice a=-16, b=20, and c=20)

t+=+%28-20+%2B-+sqrt%28+%2820%29%5E2-4%2A-16%2A20+%29%29%2F%282%2A-16%29 Plug in a=-16, b=20, and c=20



t+=+%28-20+%2B-+sqrt%28+400-4%2A-16%2A20+%29%29%2F%282%2A-16%29 Square 20 to get 400



t+=+%28-20+%2B-+sqrt%28+400%2B1280+%29%29%2F%282%2A-16%29 Multiply -4%2A20%2A-16 to get 1280



t+=+%28-20+%2B-+sqrt%28+1680+%29%29%2F%282%2A-16%29 Combine like terms in the radicand (everything under the square root)



t+=+%28-20+%2B-+4%2Asqrt%28105%29%29%2F%282%2A-16%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



t+=+%28-20+%2B-+4%2Asqrt%28105%29%29%2F-32 Multiply 2 and -16 to get -32

So now the expression breaks down into two parts

t+=+%28-20+%2B+4%2Asqrt%28105%29%29%2F-32 or t+=+%28-20+-+4%2Asqrt%28105%29%29%2F-32


Now break up the fraction


t=-20%2F-32%2B4%2Asqrt%28105%29%2F-32 or t=-20%2F-32-4%2Asqrt%28105%29%2F-32


Simplify


t=5+%2F+8-sqrt%28105%29%2F8 or t=5+%2F+8%2Bsqrt%28105%29%2F8


So these expressions approximate to

t=-0.65586884574495 or t=1.90586884574495



Since a negative time doesn't make sense, our only solution is:
t=1.90586884574495

So you are correct