SOLUTION: A toy rocket is launched from ground level. Its distance in feet from the ground in t seconds is given by the formula s(t)=-16t^2+208t (a) make a sketch of what is happening (b)

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Question 680405: A toy rocket is launched from ground level. Its distance in feet from the ground in t seconds is given by the formula s(t)=-16t^2+208t
(a) make a sketch of what is happening
(b) When will the rocket be 550 feet from the ground
(c) After how many seconds will the rocket strike the ground?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
s%28t%29=-16t%5E2%2B208t


(a) make a sketch of what is happening




(b) When will the rocket be 550 feet from the ground
550ft=-16t%5E2%2B208t
0=-16t%5E2%2B208t-550ft

t+=+%28-208+%2B-+sqrt%28+208%5E2-4%2A%28-16%29%2A%28-550%29+%29%29%2F%282%2A%28-16%29%29+

t+=+%28-208+%2B-+sqrt%28+43264-35200+%29%29%2F-32%29+

t+=+%28-208+%2B-+sqrt%28+8064+%29%29%2F-32%29+

t+=+%28-208+%2B-+89.8%29%2F-32%29+
solution:
t+=+%28-208+%2B+89.8%29%2F-32%29+
t+=+-118.2%2F-32%29+
t=3.7sec.........the rocket be 550 feet from the ground when it goes up
or
t+=+%28-208+-+89.8%29%2F-32%29+
t+=+-297.8%2F-32%29+
t=9.3sec........the rocket be 550 feet from the ground when it goes down after it reaches maximum height

(c) After how many seconds will the rocket strike the ground?

0=-16t%5E2%2B208t


t+=+%28-208+%2B-+sqrt%28+208%5E2-4%2A%28-16%29%2A0+%29%29%2F%282%2A%28-16%29%29+

t+=+%28-208+%2B-+sqrt%28+43264+%29%29%2F-32%29+

t+=+%28-208+%2B-+208%29%2F-32%29+

solution:
t+=+%28-208+%2B+208%29%2F-32%29+
t+=+0%2F-32+
t+=+0+
or
t+=+%28-208+-+208%29%2F-32%29+
t+=+-416%2F-32%29+
t=13.......the rocket strike the ground in t=13sec; on a graph, that will be a point (13,0)