Physics, 01.07.2020 16:01 robert7248

The angle between vector A = 2.00i + 3.00j and vector B is 45.0°. The scalar product of vectors A 12) and B is 7.00. If the x-component of vector B is positive, what is vector B

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Answer from: avanelson01

B = 2.67i - 0.53j

Explanation:

In order to find the vector B, you first take into account the following formula:

$\vec{A}\cdot\vec{B}=ABcos\theta$ (1)

where:

A = 2.00i + 3.00j

B = ?

θ: angle between vectors A and B = 45.0°

You use the fact that the dot product between vectors A and B is 7.00.

You calculate the magnitude of A vector as follow:

$A=\sqrt{(2.00)^2+(3.00)^2}=3.60$

Then, you solve the equation (1) for the magnitude of B:

$B=\frac{\vec{A}\cdot\vec{B}}{Acos\theta}=\frac{7.00}{3.60cos(45\°)}=2.74$

Next, you can consider that the A vector is the x axis of the coordinate system, to calculate the components of B. This means that the coordinate system is rotated an angle equivalent to the angle of A respect to the x axis.

With the previous assumption you have that the components of B are:

$B_x=Bcos\theta=(2.74)cos45\°=1.93\\\\B_y=Bsin45\°=(2.74)sin45\°=1.93$

The vector B is:

B = 1.93i + 1.93j

Next, it is necessary to rotate again the coordinate system to its original position. For that, you calculate the angle of A:

$\alpha=tan^{-1}(\frac{3.00}{2.00})=56.30$

In order to calculate the real components of B, you rotate the system 56.30°, by using the following relation:

$B_x'=B_xcos\alpha+B_ysin\alpha\\\\B_x'=1.93cos(56.30\°)+1.93sin(56.30\°)=2.67\\\\B_y'=-B_xsin\alpha+B_ycos\alpha\\\\B_y'=-1.93sin(56.30\°)+1.93cos(56.30\°)=-0.53$

The vector B is:

B = 2.67i - 0.53j

Answer from: Quest

-first use of geothermal energy occurred more than 10,000 years ago in north america by american paleo-indians

-the first industrial use of geothermal energy began near pisa, italy in late 18th century

-in 1904, italian scientist piero ginori conti invented the first geothermal electric power plant in which steam was used to generate the power

-with the above experiment, the first geothermal plant in usa started in 1922 with a capacity of 250 kilowatts

-however, in 1946 first ground-source geothermal heat pump installed at commonwealth building in portland, oregon

-during the 1960’s, pacific gas and electric began operation of first large scale geothermal power plant in san francisco, producing 11 megawatts

-in 1973, when oil crisis began many countries began looking for renewable energy sources and by 1980’s geothermal heat pumps (ghp) started gaining popularity in order to reduce heating and cooling costs

-as effect of climate change started showing results, governments of various countries joined hands to fight against it, for which kyoto protocol was signed in japan in 1997, laid out emission targets for rich countries and required that they transfer funds and technology to developing countries, 184 countries have ratified it

hope this

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