SOLUTION: The height of an object thrown upward with an initial velocity of 96 feet per second is given by the formula h = −16t2 + 96t, where t is the time in seconds. a) How long will

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The height of an object thrown upward with an initial velocity of 96 feet per second is given by the formula h = −16t2 + 96t, where t is the time in seconds. a) How long will      Log On


   

Question 1160607: The height of an object thrown upward with an initial velocity of 96 feet per second is given by the formula h = −16t2 + 96t, where t is the time in seconds.
a) How long will it take the object to reach a height of 144 feet?
b) How long will it take the object to return to the point of departure?
Found 3 solutions by Alan3354, MathLover1, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The height of an object thrown upward with an initial velocity of 96 feet per second is given by the formula h = −16t2 + 96t, where t is the time in seconds.
a) How long will it take the object to reach a height of 144 feet?
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h = −16t2 + 96t = 144
Solve for t.
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b) How long will it take the object to return to the point of departure?
h = −16t2 + 96t = 0
Solve for t.
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Use ^ (Shift 6) for exponents.
h = −16t^2 + 96t

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
You have this quadratic equation:

h+=+-16t%5E2+%2B+96t
16t%5E2+-96t+%2B+h+=+0

The solution to this is always

t+=+%2896+%2B-+sqrt%2896%5E2+-+64h%29%29%2F64

and if h+=144ft, then
t+=+%2896+%2B-+sqrt%2896%5E2+-+64%2A144%29%29%2F64
t+=+%2896+%2B-+sqrt%289216+-+9216%29%29%2F64
t+=+%2896+%2B-+sqrt%280%29%29%2F64
t+=+96%2F64
t+=+1.5s

If you want to get back to the point of departure, that's when h=0.
the first problem is actually the midpoint of flight, and it will take +1.5s more to get back to the point of departure
total time is t+=+3s
or, do it this way:

0=+-16t%5E2+%2B+96t
0=+-16t%28t+-+6%29

solutions:
0=-16t->t=0
0=+%28t+-+6%29-> t=6



and the midpoint between t=0 and t=6 will be t+=+3s.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The height of an object thrown upward with an initial velocity of 96 feet per second is given by the formula h = −16t2 + 96t, where t is the time in seconds.
a) How long will it take the object to reach a height of 144 feet?
b) How long will it take the object to return to the point of departure? 
She's WRONG, as usual, and AGAIN, making these SIMPLE problems SO, SO complex!!

It's NEVER what she states. You'll confuse yourself and most times end up with wrong answers if you should follow what she says!

Don't say I didn't WARN you!!

matrix%281%2C3%2C+h%2C+%22=%22%2C+-+16t%5E2+%2B+96t%29

matrix%281%2C3%2C+144%2C+%22=%22%2C+-+16t%5E2+%2B+96t%29 ------ Substituting 144 for h



Time it'll take for the object to reach a height of 144 feet is the point where,