SOLUTION: Please help me solve this equation. The height h of a missile after t seconds, when fired straight up with an initial height of 2 feet, can be modeled by the function h(t)=-16t^2

Algebra ->  Probability-and-statistics -> SOLUTION: Please help me solve this equation. The height h of a missile after t seconds, when fired straight up with an initial height of 2 feet, can be modeled by the function h(t)=-16t^2      Log On


   

Question 1159584: Please help me solve this equation.
The height h of a missile after t seconds, when fired straight up with an initial height of 2 feet, can be modeled by the function h(t)=-16t^2+150t+2
A.) When will the missile be 250 feet?
B.) When will the missile be at it's maximum height?
C.) What is the maximum height of the missile?
D.)Will the missile ever reach a height of 400ft?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!


The height h+of a missile after t seconds, when fired straight up with an initial height of 2 feet, can be modeled by the function
h%28t%29=-16t%5E2%2B150t%2B2+
A.) When will the missile be 250+feet?
->h=250+
250=-16t%5E2%2B150t%2B2+
16t%5E2-150t-2+%2B250=0
16t%5E2-150t%2B248=0......use quadratic formula

t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
t+=+%28-%28-150%29+%2B-+sqrt%28+%28-150%29%5E2-4%2A16%2A248+%29%29%2F%282%2A16%29+
t+=+%28150+%2B-+sqrt%28+22500-15872+%29%29%2F32+
t+=+%28150+%2B-+sqrt%28+6628+%29%29%2F32+
t+=+%28150+%2B-+81.413%29%2F32+
solutions:
t+=+%28150+%2B+81.413%29%2F32+ ->t+=7.23+
t+=+%28150+-+81.413%29%2F32+ ->t+=2.14+
fired straight up the missile will be 250+ feet high in t+=2.14+ seconds, and on way back again in t+=7.23+ seconds


B.) When will the missile be at it's maximum height?
if a is negative, the parabola opens down and maximum is at vertex
so, write your equation in vertex form:
h%28t%29=-16t%5E2%2B150t%2B2+
h%28t%29=-16%28t%5E2-%28150%2F16%29t%29%2B2+.....complete square
h%28t%29=-16%28t%5E2-%2875%2F8%29t%2Bb%5E2%29-%28-16%29b%5E2%2B2+......b=%2875%2F8%29%2F2=%2875%2F16%29
h%28t%29=-16%28t%5E2-%2875%2F8%29t%2B%2875%2F16%29%5E2%29%2B16%2875%2F16%29%5E2%2B2+
h%28t%29=-16%28t-75%2F16%29%5E2%2B5657%2F16
h%28t%29=-16%28t-75%2F16%29%5E2%2B353.5625
-> h=75%2F16=4.7 and k=353.6
vertex: (4.7,353.6)
the missile will be at it's maximum height in 4.7 seconds


C.) What is the maximum height of the missile?
h=353.6ft

D.)Will the missile ever reach a height of 400ft?
h=400ft
400=-16t%5E2%2B150t%2B2+
16t%5E2-150t-2+%2B400=0
16t%5E2-150t+%2B398=0.......check discriminant
If b%5E2%E2%88%924ac+%3C+0 the equation has no real number solutions, but it does have complex solutions
%28-150%29%5E2-4%2A16%2A39%3C0
-2972%3C+0-> true
so, the missile will never reach a height of 400ft