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vovikov84 [41]
3 years ago
14

A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 6 ft from the path and is kept fo

cused on the man. At what rate is the searchlight rotating when the man is 8 ft from the point on the path closest to the searchlight
Physics
1 answer:
BARSIC [14]3 years ago
4 0

We are given that,

\frac{dx}{dt} = 4ft/s

We need to find \frac{d\theta}{dt} when x=8ft

The equation that relates x and \theta can be written as,

\frac{x}{6} tan\theta

x = 6tan\theta

Differentiating each side with respect to t, we get,

\frac{dx}{dt} = \frac{dx}{d\theta} \cdot \frac{d\theta}{dt}

\frac{dx}{dt} = (6sec^2\theta)\cdot \frac{d\theta}{dt}

\frac{d\theta}{dt} = \frac{1}{6sec^2\theta} \cdot \frac{dx}{dt}

Replacing the value of the velocity

\frac{d\theta}{dt} = \frac{1}{6} cos^2\theta (4)^2

\frac{d\theta}{dt} = \frac{8}{3} cos^2\theta

The value of cos \theta could be found if we know the length of the beam. With this value the equation can be approximated to the relationship between the sides of the triangle that is being formed in order to obtain the numerical value. If this relation is known for the value of x = 6ft, the mathematical relation is obtained. I will add a numerical example (although the answer would end in the previous point) If the length of the beam was 10, then we would have to

cos\theta = \frac{6}{10}

\frac{d\theta}{dt} = \frac{8}{3} (\frac{6}{10})^2

\frac{d\theta}{dt} = \frac{24}{25}

Search light is rotating at a rate of 0.96rad/s

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The ratio of their amplitudes will be 2.41.

To find the answer, we have to know more about the simple harmonic motion.

<h3>How to find the ratio of their amplitudes?</h3>
  • It is given that,

                        E_1=5.8E_2\\m_1=m_2 \\\omega_1=\omega_2

  • We have the relation between these quantities and amplitudes as,

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  • Here, for both the oscillation, k will be same.
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                      \frac{A_1}{A_2} =\sqrt{\frac{E_1}{E_2} } =\sqrt{\frac{5.8E_2}{E_2} } =2.41

Thus, we can conclude that, the ratio of their amplitudes will be 2.41.

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How does mass effect acceleration
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Option A is correct.

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It is represented as K and is shown mathematically through the heat flux at turbulent flow

q = vCρT' = - K (∂T/∂y)

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q = the rate of thermal energy transport by turbulent eddies.

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This includes sharp changes in fluid pressure and velocity of flow which is evident in eddies that come about in the enhanced mixing of fluids.

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How many joules of heat must be transferred to a 410-g aluminum pizza pan to raise its temperature from 32oC to 232oC? The speci
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Answer:

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Q = mc*(T2 - T1)

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m = mass (in g)

c = specific heat capacity (in J/g-k)

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Substituting, we find the force of gravity on the student:

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