SOLUTION: One piece of ash was ejected from a volcano with a initial velocity of 336ft/sec. The heigh H in feet is given by the equation H=-16t^2+336t where T is the time in seconds. When d

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: One piece of ash was ejected from a volcano with a initial velocity of 336ft/sec. The heigh H in feet is given by the equation H=-16t^2+336t where T is the time in seconds. When d      Log On


   

Question 1160350: One piece of ash was ejected from a volcano with a initial velocity of 336ft/sec. The heigh H in feet is given by the equation H=-16t^2+336t where T is the time in seconds.
When does the ash projectile reach its maximim height?
It's the vertex of the parabola at t = -b/2a
Solve for t
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What is its maximum height?
Sub t at the vertex.
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when does the ash projectile return to the ground?
When -16t^2 + 336t = 0
Which is 2 times the t at the vertex.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

H=-16t%5E2%2B336t+where t is the time in seconds.
When does the ash projectile reach its maximum height?
It's the vertex of the parabola at t+=+-b%2F2a
in your case b=336 and a=-16
then
t+=+-336%2F%282%28-16%29%29
t+=+-336%2F%28-32%29
t+=+336%2F32
t+=21%2F2


What is its maximum height?
Sub t+at the vertex.
H=-16%2821%2F2%29%5E2%2B336%2821%2F2%29+
H=-16%28441%2F4%29%2B3528
H=-1764%2B3528
H=1764
max H=+1764+at t+=+21%2F2

when does the ash projectile return to the ground?
When -16t%5E2+%2B+336t+=+0
Which is 2 times the+t at the vertex
t+at the vertex: t+=21%2F2
2 times the t at the vertex: t=2%2821%2F2%29=21
the ash projectile return to the ground in 21 seconds