SOLUTION: A man launches a projectile from top of 120' building. The height of the projectile above the ground is given by h=120+8t-16t2 (power of 2) where t = time in seconds after launch

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: A man launches a projectile from top of 120' building. The height of the projectile above the ground is given by h=120+8t-16t2 (power of 2) where t = time in seconds after launch      Log On


   

Question 92897: A man launches a projectile from top of 120' building. The height of the projectile above the ground is given by h=120+8t-16t2 (power of 2) where t = time in seconds after launch. WHEN WILL THE PROJECTILE BE 60 FEET OFF THE GROUND
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
h=120%2B8t-16t%5E2

60=120%2B8t-16t%5E2 Plug in h=60

0=-16t%5E2%2B8t%2B60 Subtract 60 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%2B8%2At%2B60=0 ( notice a=-16, b=8, and c=60)

t+=+%28-8+%2B-+sqrt%28+%288%29%5E2-4%2A-16%2A60+%29%29%2F%282%2A-16%29 Plug in a=-16, b=8, and c=60



t+=+%28-8+%2B-+sqrt%28+64-4%2A-16%2A60+%29%29%2F%282%2A-16%29 Square 8 to get 64



t+=+%28-8+%2B-+sqrt%28+64%2B3840+%29%29%2F%282%2A-16%29 Multiply -4%2A60%2A-16 to get 3840



t+=+%28-8+%2B-+sqrt%28+3904+%29%29%2F%282%2A-16%29 Combine like terms in the radicand (everything under the square root)



t+=+%28-8+%2B-+8%2Asqrt%2861%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+=+%28-8+%2B-+8%2Asqrt%2861%29%29%2F-32 Multiply 2 and -16 to get -32

So now the expression breaks down into two parts

t+=+%28-8+%2B+8%2Asqrt%2861%29%29%2F-32 or t+=+%28-8+-+8%2Asqrt%2861%29%29%2F-32


Now break up the fraction


t=-8%2F-32%2B8%2Asqrt%2861%29%2F-32 or t=-8%2F-32-8%2Asqrt%2861%29%2F-32


Simplify


t=1+%2F+4-sqrt%2861%29%2F4 or t=1+%2F+4%2Bsqrt%2861%29%2F4


So these expressions approximate to

t=-1.70256241897666 or t=2.20256241897666


So our solutions are:
t=-1.70256241897666 or t=2.20256241897666

Since a negative time doesn't make much sense, our only solution is

t=2.20256241897666

which is about 2.2 seconds