SOLUTION: A rocket is launched from atop a 101-foot cliff with an initial velocity of 116ft/s. a. Substitute the values into the vertical motion formula h=-16t^2+vt+c. Let h=0 b.Use the qu

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A rocket is launched from atop a 101-foot cliff with an initial velocity of 116ft/s. a. Substitute the values into the vertical motion formula h=-16t^2+vt+c. Let h=0 b.Use the qu      Log On


   

Question 195679: A rocket is launched from atop a 101-foot cliff with an initial velocity of 116ft/s.
a. Substitute the values into the vertical motion formula h=-16t^2+vt+c. Let h=0
b.Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched Round to the nearest tenth of a second
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The initial velocity is 116 so v+=+116


The initial height is 101 so c+=+101


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a)


h=-16t%5E2%2Bvt%2Bc Start with the given equation.


h=-16t%5E2%2B116t%2B101 Plug in v=116 and c=101


0=-16t%5E2%2B116t%2B101 Plug in h=0 (i.e., replace h with 0)

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b)


Refer to part A above.


Notice we have a quadratic equation in the form of 0=at%5E2%2Bbt%2Bc where a=-16, b=116, and c=101


Let's use the quadratic formula to solve for t


t+=+%28-%28116%29+%2B-+sqrt%28+%28116%29%5E2-4%28-16%29%28101%29+%29%29%2F%282%28-16%29%29 Plug in a=-16, b=116, and c=101


t+=+%28-116+%2B-+sqrt%28+13456-4%28-16%29%28101%29+%29%29%2F%282%28-16%29%29 Square 116 to get 13456.


t+=+%28-116+%2B-+sqrt%28+13456--6464+%29%29%2F%282%28-16%29%29 Multiply 4%28-16%29%28101%29 to get -6464


t+=+%28-116+%2B-+sqrt%28+13456%2B6464+%29%29%2F%282%28-16%29%29 Rewrite sqrt%2813456--6464%29 as sqrt%2813456%2B6464%29


t+=+%28-116+%2B-+sqrt%28+19920+%29%29%2F%282%28-16%29%29 Add 13456 to 6464 to get 19920


t+=+%28-116+%2B-+sqrt%28+19920+%29%29%2F%28-32%29 Multiply 2 and -16 to get -32.


t+=+%28-116+%2B-+4%2Asqrt%281245%29%29%2F%28-32%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


t+=+%28-116%2B4%2Asqrt%281245%29%29%2F%28-32%29 or t+=+%28-116-4%2Asqrt%281245%29%29%2F%28-32%29 Break up the expression.


t+=+%2829-sqrt%281245%29%29%2F%288%29 or t+=+%2829%2Bsqrt%281245%29%29%2F%288%29 Reduce


So the exact roots are t+=+%2829-sqrt%281245%29%29%2F%288%29 or t+=+%2829%2Bsqrt%281245%29%29%2F%288%29


which approximate to t=-0.78556969109433 or t=8.03556969109433


Since a negative time value doesn't make sense, the only practical root is approximately t=8.03556969109433


This rounds to one decimal place to get t+=+%228.0%22


So it takes about 8.0 seconds for the rocket to hit the ground.