SOLUTION: A stone is tossed from a bridge into the river below. Its path is represented by h = -2t^2 + 7t + 9, where h is height, in metres, and t is time, in seconds. Find the maximum heig

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A stone is tossed from a bridge into the river below. Its path is represented by h = -2t^2 + 7t + 9, where h is height, in metres, and t is time, in seconds. Find the maximum heig      Log On


   

Question 1188443: A stone is tossed from a bridge into the river below. Its path is represented by h = -2t^2 + 7t + 9, where h is height, in metres, and t is time, in seconds.
Find the maximum height reached by the stone.
How many seconds does it take to reach the maximum height?
How many seconds does it take for the stone to reach the water?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

h+=+-2t%5E2+%2B+7t+%2B+9, where h is height, in metres, and t+is time, in seconds.
Find the maximum height reached by the stone.
since you have a parabola that opens downward, maximum will be at vertex
so, rewrite equation in vertx form by completing square
h=%28-2t%5E2+%2B+7t%29+%2B+9......factor out -2
h=-2%28t%5E2+-+%287%2F2%29t%29+%2B+9
h=-2%28t%5E2+-+%287%2F2%29t%2Bb%5E2%29+-%28-2b%5E2%29%2B+9.............b=%287%2F2%29%2F2=7%2F4%29
h=-2%28t%5E2+-+%287%2F2%29t%2B%287%2F4%29%5E2%29+%2B2%287%2F4%29%5E2%2B+9
h=-2%28t+-+7%2F4%29%5E2+%2B2%2849%2F16%29%2B+9
h=-2%28t+-+7%2F4%29%5E2+%2B121%2F8
=> vertex is at (7/4,121/8)
so, the maximum height reached by the stone is h=121%2F8 or h=15.125
How many seconds does it take to reach the maximum height?
h+=+-2t%5E2+%2B+7t+%2B+9....plug in h=15.125
15.125+=+-2t%5E2+%2B+7t+%2B+9........solve for t
2t%5E2+-+7t+%2B+6.125+=+0.....using quadratic formula we get
t=1.75seconds
How many seconds does it take for the stone to reach the water?
0+=+-2t%5E2+%2B+7t+%2B+9....plug in h=0
0+=+-2t%5E2+%2B+7t+%2B+9......factor
0+=+-%28t+%2B+1%29+%282t+-+9%29
solutions:
t+=+-1-> disregard negative time
t+=+9%2F2
t+=+4.5
it takes 4.5seconds for the stone to reach the water

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
A stone is tossed from a bridge into the river below. Its path is represented by h = -2t^2 + 7t + 9,
where h is height, in metres, and t is time, in seconds.
Find the maximum height reached by the stone.
How many seconds does it take to reach the maximum height?
How many seconds does it take for the stone to reach the water?
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The equation in your post,  describing the height as a function of time,   I S   I N C O R R E C T.

The correct equation is  TOTALLY  DIFFERENT.


How this equation is presented in the post, it makes it clear that the person who created / composed this problem,
is mathematically  ILLITERATE  and unfamiliar with the corresponding sections of  Math and  Physics.

So,  solving this problem,  in the form as it is presented in the post,  is  NONSENSE.


Due to this reason,  the response by @MathLover1 is  NONSENSE  and  BAD  TEACHING,  too.


To learn the subject,  read the lessons
    - Introductory lesson on a projectile thrown-shot-launched vertically up
    - Problem on a projectile moving vertically up and down
    - Problem on a toy rocket launched vertically up from a tall platform

Consider these lessons as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.
Read them attentively and learn how to solve this type of problems once and for all.

Start reading from the very first lesson.