SOLUTION: Herman arranged a game of water balloon volleyball for his daughter’s birthday party. Suppose the balloon has a height of h metres, t seconds after it is tossed, as defined by h =
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Question 1049249: Herman arranged a game of water balloon volleyball for his daughter’s birthday party. Suppose the balloon has a height of h metres, t seconds after it is tossed, as defined by h = -5t^2 + 12t + 1.
a) Write an equation that shows how many seconds will pass before the balloon hits the ground. Solve this equation,rounded to the nearest hundredth of a second.
b) what is the maximum height reached by the balloon? When does it reach this height?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Herman arranged a game of water balloon volleyball for his daughter’s birthday party. Suppose the balloon has a height of h metres, t seconds after it is tossed, as defined by h = -5t^2 + 12t + 1.
a) Write an equation that shows how many seconds will pass before the balloon hits the ground. Solve this equation,rounded to the nearest hundredth of a second.
Height = zero when the balloon hits the ground.
Solve: -5t^2+12t+1 = 0
t = 2.48 seconds
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b) what is the maximum height reached by the balloon? When does it reach this height?
Max occurs when t = -b/(2a) = -12/(2*-5) = 6/5
Max height = f(6/5) = -5(6/5)^2+12(6/5)+1 = 8.2 metres
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Cheers,
Stan H.
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Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
(a)
---------------------------
The ball is tossed at
This gives you:
They are saying that the ball is tossed from a height
of meter
---------------------------
You want to know the time in seconds when
( balloon hits the ground )
Use the quadratic formula
( time has to come out positive )
sec
The balloon hits the ground in 2.48 sec
----------------------------------------
(b)
The -value at the maximum is:
Plug this value back into equation
The maximm height is 8.2 m which it will
reach in 1.2 sec
------------------------
check:
Here's the plot:
My numbers look pretty close
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