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statuscvo [17]
3 years ago
10

I throw a stone off a cliff 32 feet above the water.  The height of the stone in terms of time (in seconds) is given by h(t) = -

16t2 + 128t + 32.  At what time will the stone splash into the water? Round your answer to nearest tenth of a second
Physics
1 answer:
devlian [24]3 years ago
5 0
<span>Your equation for the height of the stone at any time is   h(t) = -16t2<span> + 128t + 32 .

From your equation, we can tell that you're defining the upward direction as
positive.  We can also tell that you threw the stone upward, with an initial speed
as it left your hand of 128 feet per second, about 87 miles per hour ... a mighty toss indeed, and I think there's a man from the Chicago Cubs waiting outside
who'd like to talk to you.

Anyway, When the stone splashes into the water,  h(t) = 0 .
</span></span>
<span>-16t²<span> + 128t + 32 = 0</span></span>

Divide each side by -16 :

t² - 8t - 2 = 0

I don't see any easy way to factor the expression on the left,
so I have to use the quadratic formula to solve this equation.

t = 4 plus and minus √18 .

t = +8.24 seconds
t = -0.24 second

Mathematically, both numbers are valid solutions.But when you apply
the equation to a real world situation, only the positive 't' makes sense.
So  <u> t = 8.24 seconds</u>.
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Kinetic energy depends on the height of an object above the ground?
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A man walks 7 km, east in 2 hours and 2 km in 1 hour in the same direction. a) what is
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Explanation:

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If the rectangular barge is 3.0 m by 20.0 m and sits 0.70 m deep in the harbor, how deep will it sit in the river?
leva [86]

The harbour contains salt water while the river contains fresh water. So assuming that the densities of fresh water and salt water are:

density (salt water) = 1029 kg / m^3

density (fresh water) = 1000 kg / m^3

The amount of water (in mass) displaced by the barge should be equal in two waters.

mass displaced (salt water) = mass displaced (fresh water)

Since mass is also the product of density and volume, therefore:

<span>[density * volume]_salt water = [density * volume]_fresh water                 ---> 1</span>

 

First we calculate the amount of volume displaced in the harbour (salt water):

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V = 42 m^3 of salt water

Plugging in the values into equation 1:

1029 kg / m^3 * 42 m^3 = 1000 kg/m^3 * Volume fresh water

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Tina has lost 24 pounds in total during the 13 weeks

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