SOLUTION: Ben is an excellent juggler. He juggles at a height of 4 feet and at a speed of 30 feet per second. A)Set up an equation where height is a function of time. B) How many seco

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Question 1010949: Ben is an excellent juggler. He juggles at a height of 4 feet and at a speed of 30 feet per second.
A)Set up an equation where height is a function of time.
B) How many seconds would it take for one of the balls to hit the ground if Ben missed it?

I got 0 = -16t +4t but I didn't know how to set it up after that or how to solve it. I'd really like some help with this. Thank you!
Found 2 solutions by stanbon, rothauserc:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Ben is an excellent juggler. He juggles at a height of 4 feet and at a speed of 30 feet per second.
A)Set up an equation where height is a function of time.
B) How many seconds would it take for one of the balls to hit the ground if Ben missed it?
I got 0 = -16t +4t but I didn't know how to set it up after that or how to solve it. I'd really like some help with this. Thank you!
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A) h(t) = -16t^2 + 4t +4
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B) Solve:
-16t^2 + 4t + 4 = 0
-4t^2 + t + 1 = 0
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t = [-1 +- sqrt(1^2 - 4*-4*1)]/(-8)
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t = [-1 +- sqrt(17)]/(-8)
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t = [-1 - sqrt(17)]/(-8)
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t = 0.64 seconds
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Cheers,
Stan H.
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Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
A) the general formula for the height of a thrown projectile after t seconds is:
s(t) = –gt^2 + v0t + h0 where g is the force of gravity(4.9 if working in meters and 16 if working in feet, v0 is the initial velocity of the projectile, h0 is the height when the projectile is released
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B) for our problem, g=16, vo=30, h0=4 and s(t) = 0
0 = -16t^2 +30t +4
factor the polynomial
(16t +2)*(-t +2) = 0
there are two solutions
1) 16t +2 = 0
t = -1/8
2) -t +2 = 0
t = 2
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we reject the negative value for t since time does not run backwards
our solution is
the ball hits the ground after 2 seconds