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charle [14.2K]
3 years ago
10

The height of the tide measured at a seaside community varies according to the number of hours t after midnight. If the height h

, in feet, is currently given by the equation h=-1/2 t^2+6t-9, when will the tide first be at 6 ft?
Physics
1 answer:
antoniya [11.8K]3 years ago
6 0

Explanation:

Given that, the height of the tide measured at a seaside community varies according to the number of hours t after midnight. The height is given by the equation as :

h=-\dfrac{1}{2}t^2+6t-9

When the tide first be at 6 ft, put h = 6 ft in above equation as :

-\dfrac{1}{2}t^2+6t-9=6

-t^2+12t-18=0

On solving the above equation to find the value of t. It is equal to :

t = 3.551 seconds

or

t = 8.449 seconds

So, the tide of 6 ft is at  3.551 seconds and 8.449 seconds. Hence, this is the required solution.

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3 years ago
By method of dimension show that the following equation are homogenous.
il63 [147K]

Answer:

Proof in explanataion

Explanation:

The basic dimensions are as follows:

MASS = M

LENGTH = L

TIME = T

i)

Given equation is:

H = \frac{u^2Sin^2\phi}{2g}

where,

H = height (meters)

u = speed (m/s)

g = acceleration due to gravity (m/s²)

Sin Ф = constant (no unit)

So there dimensions will be:

H = [L]

u = [LT⁻¹]

g = [LT⁻²]

Sin Ф = no dimension

Therefore,

[L] = \frac{[LT^{-1}]^2}{[LT^{-2}]}\\\\\ [L] = [L^{(2-1)}T^{(-2+2)}]

<u>[L] = [L]</u>

Hence, the equation is proven to be homogenous.

ii)

F = \frac{Gm_1m_2}{r^2}\\\\

where,

F = Force = Newton = kg.m/s² = [MLT⁻²]

G = Gravitational Constant = N.m²/kg² = (kg.m/s²)m²/kg² = m³/kg.s²

G = [M⁻¹L³T⁻²]

m₁ = m₂ = mass = kg = [M]

r = distance = m = [L]

Therefore,

[MLT^{-2}] = \frac{[M^{-1}L^{3}T^{-2}][M][M]}{[L]^2}\\\\\ [MLT^{-2}] = [M^{(-1+1+1)}L^{(3-2)}T^{-2}]\\\\

<u>[MLT⁻²] = [MLT⁻²]</u>

Hence, the equation is proven to be homogenous.

8 0
3 years ago
If a 4 engine jet accelerates down a runway at 8.7 m/s^2, Suppose now that all 4 engins are operational on the jet from the prev
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Answer:

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One of the first propulsion characteristics given in the example is that all engines are equal.

In this way if we have 4 engines running at the same time, it means that its capacity is 100%.

Under this premise, if 100% is found, the Jet is capable of reaching a speed of 8.7m / s ^ 2.

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To do this then we make a simple equivalence,

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Answer:

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Explanation:

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