SOLUTION: 3. A projectile is fired upward from a platform in such a way that the object will miss the platform on the way down. If the height of the platform is 28 ft and the initial velcoit

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 3. A projectile is fired upward from a platform in such a way that the object will miss the platform on the way down. If the height of the platform is 28 ft and the initial velcoit      Log On


   

Question 93468: 3. A projectile is fired upward from a platform in such a way that the object will miss the platform on the way down. If the height of the platform is 28 ft and the initial velcoity is 204ft/sec, the height is given by h=-16t^2+204t+28 When will the projectile hit the ground?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

To find out when the projectile will hit the ground, let h=0 and solve for t

0=-16t%5E2%2B204t%2B28 Plug in h=0


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%2B204%2At%2B28=0 ( notice a=-16, b=204, and c=28)

t+=+%28-204+%2B-+sqrt%28+%28204%29%5E2-4%2A-16%2A28+%29%29%2F%282%2A-16%29 Plug in a=-16, b=204, and c=28



t+=+%28-204+%2B-+sqrt%28+41616-4%2A-16%2A28+%29%29%2F%282%2A-16%29 Square 204 to get 41616



t+=+%28-204+%2B-+sqrt%28+41616%2B1792+%29%29%2F%282%2A-16%29 Multiply -4%2A28%2A-16 to get 1792



t+=+%28-204+%2B-+sqrt%28+43408+%29%29%2F%282%2A-16%29 Combine like terms in the radicand (everything under the square root)



t+=+%28-204+%2B-+4%2Asqrt%282713%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+=+%28-204+%2B-+4%2Asqrt%282713%29%29%2F-32 Multiply 2 and -16 to get -32

So now the expression breaks down into two parts

t+=+%28-204+%2B+4%2Asqrt%282713%29%29%2F-32 or t+=+%28-204+-+4%2Asqrt%282713%29%29%2F-32


Now break up the fraction


t=-204%2F-32%2B4%2Asqrt%282713%29%2F-32 or t=-204%2F-32-4%2Asqrt%282713%29%2F-32


Simplify


t=51+%2F+8-sqrt%282713%29%2F8 or t=51+%2F+8%2Bsqrt%282713%29%2F8


So these expressions approximate to

t=-0.135808321552709 or t=12.8858083215527


So our possible solutions are:
t=-0.135808321552709 or t=12.8858083215527


Since a negative time doesn't make sense, our only solution is t=12.8858083215527

So the projectile will hit the ground at about 12.89 seconds