SOLUTION: Help please! I'm so confused by this problem... if an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Help please! I'm so confused by this problem... if an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time      Log On


   

Question 763757: Help please! I'm so confused by this problem...
if an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time t is given by: h=-16t^2+vt+s
(where h and s are in ft, t is in seconds and v is in ft/sec)
a package is thrown downward with an initial velocity of -5ft/sec from a helicopter at 300 ft.
a) what is the height of the package in 2 sec?
b) how long does it take to hit the ground?
Found 2 solutions by solver91311, rothauserc:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




For ft/sec and feet



Then for seconds



Do the arithmetic

The ground is so:



Solve the quadratic for .

Discard the negative root.

John

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Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
f an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time t is given by: h=-16t^2+vt+s
(where h and s are in ft, t is in seconds and v is in ft/sec)
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note that an object thrown upward would have a positive value for the initial velocity (v)....in our case the object is thrown downward so the value for v is negative.
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a) what is height after 2 seconds?
h = -16*t^2 +v*t + s
h = -16*(2^2) -5*2 + 300
h = -64 -10 +300
h = 226 feet after 2 seconds
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b) how long does it take to hit the ground? that is h=0
0 = -16t^2 -5t + 300
divide by -1 and we get
0 = 16t^2 +5 - 300
use quadratic formula
t = (-5+sqrt(25-4*16*-300)) / 32 = 4.18
t = (-5-sqrt(25-4*16*-300)) / 32 = -4.49
t reaches the ground in 4.18 seconds
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