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aliina [53]
3 years ago
12

A cyclist rides 4.0 km due west, then 12.0 km 33° west of north. From this point she rides 9.0 km due east. What is the final di

splacement from where the cyclist started (in km)? (Express your answer in vector form. Assume the +x-axis is to the east, and t
Physics
1 answer:
IgorC [24]3 years ago
5 0

Answer:

\mathbf{r = (-5.064   \ \hat i + 6.536 \ \hat j) km}

Explanation:

Given that:

A cyclist rides 4.0 km due west, then 12.0 km 33° west of north. From this point she rides 9.0 km due east.

Let:

r_1 = 4.0  \ km \ due \ west \\ \\ r_2 = 12.0 \  km \  \ \ \ \  \theta = 33^0 \ west \ of \ north \\ \\ r_3 = 9.0 \ km \ due  \ east

Assuming that:

east is the + x axis  and has a unit vector of \hat i

north is the +y axis and has a unit vector of \hat j

west is the - x axis and has a unit vector of -\hat {i}

south is the - y axis and has a unit vector of -\hat j

The displacement r_x in a given direction of x can be expressed by the formula:

r_x = \sum r_i

r_x = -4-12 cos (33)+9

r_x = - 5.064 \ km

The displacement r_y in a given direction of y can be expressed by the formula:

r_y = \sum r_j

r_y = 12  \ \ * s in (33)

r_y = 6.536 \ km

The final displacement can be expressed by the relation;

r = r_x \hat i + r_y \hat j

\mathbf{r = (-5.064   \ \hat i + 6.536 \ \hat j) km}

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Explanation:

Formula for maximum efficiency of a Carnot refrigerator is as follows.

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And, formula for maximum efficiency of Carnot refrigerator is as follows.

     \frac{W}{Q_{C_{2}}} = \frac{T_{H_{2}} - T_{C_{2}}}{T_{C_{2}}} ...... (2)

Now, equating both equations (1) and (2) as follows.

 Q_{C_{2}} \frac{T_{H_{2}} - T_{C_{2}}}{T_{C_{2}}} = Q_{H_{1}} \frac{T_{H_{1}} - T_{C_{1}}}{T_{H_{1}}}        

        \gamma = \frac{Q_{C_{2}}}{Q_{H_{1}}}

                    = \frac{T_{C_{2}}}{T_{H_{1}}} (\frac{T_{H_{1}} - T_{C_{1}}}{T_{H_{2}} - T_{C_{2}}})

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Thus, we can conclude that the ratio of heat extracted by the refrigerator ("cooling load") to the heat delivered to the engine ("heating load") is 2.5.

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3 years ago
At what wavelength would a star radiate the greatest amount of energy if the star has a surface temperature of 60,000 K?
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Answer:

\lambda=4.81\times 10^{-8}\ m

Explanation:

We have,

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\lambda T=2.89\times 10^{-3}

Here,

\lambda = wavelength

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So, the wavelength of the star is 4.81\times 10^{-8}\ m.

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Answer:

1

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Heat is added to an open pan of water at 100.0°c, vaporizing the water. the expanding steam that results does 43.0 kj of work, a
vampirchik [111]
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sergij07 [2.7K]

Answer:

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I is the current through the wire

μ is the permeability of free space or vacuum

R is the distance between the point and the wire, in this case is = a

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