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Solar Panels have to be installed carefu...

Solar Panels have to be installed carefully so that the tilt of the roof, and the direction to the sun, produce the largest possible electrical power in the solar panels.
A surveyor uses his instrument to determine the coordinates of the four corners of a roof where solar panels are to be mounted. In the picture , suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters `P_(1) (6,8,4) , P_(2) (21,8,4), P_(3) (21,16,10)` and `P_(4)(6,16,10)`

What is the angle between vectors ?`vecN` and `vecS` ? What is the elevation angle of the sun above the plane of the roof? (COS `51^(@)` =0.629 )

Text Solution

Verified by Experts

The correct Answer is:
`sqrt((-90)^(2)+120^(2))=sqrt(8100+14400)=sqrt(22500)=150`
Answer of second part: `vecF= 910 (1//2hati -6//7hatj +1//7hatk) = 455hati – 780hatj+ 130hatk. `
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Solar Panels have to be installed carefully so that the tilt of the roof, and the direction to the sun, produce the largest possible electrical power in the solar panels. A surveyor uses his instrument to determine the coordinates of the four corners of a roof where solar panels are to be mounted. In the picture , suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters P_(1) (6,8,4) , P_(2) (21,8,4), P_(3) (21,16,10) and P_(4)(6,16,10) What are the magnitudes of the vectors vecA and vecB and in what units?

Solar Panels have to be installed carefully so that the tilt of the roof, and the direction to the sun, produce the largest possible electrical power in the solar panels. A surveyor uses his instrument to determine the coordinates of the four corners of a roof where solar panels are to be mounted. In the picture , suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters P_(1) (6,8,4) , P_(2) (21,8,4), P_(3) (21,16,10) and P_(4)(6,16,10) What are the components to the vector vecN perpendicular to vecA and and vecB the surface of the roof?

Solar Panels have to be installed carefully so that the tilt of the roof, and the direction to the sun, produce the largest possible electrical power in the solar panels. A surveyor uses his instrument to determine the coordinates of the four corners of a roof where solar panels are to be mounted. In the picture , suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters P_(1) (6,8,4) , P_(2) (21,8,4), P_(3) (21,16,10) and P_(4)(6,16,10) Write the vector in standard notation with hati,hatj and hatk (where hati, hatj and hatk are the unit vectors along the three axes).

Solar Panels have to be installed carefully so that the tilt of the roof, and the direction to the sun, produce the largest possible electrical power in the solar panels. A surveyor uses his instrument to determine the coordinates of the four corners of a roof where solar panels are to be mounted. In the picture , suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters P_(1) (6,8,4) , P_(2) (21,8,4), P_(3) (21,16,10) and P_(4)(6,16,10) What is the magnitude of vecN and its units? The sun is located along the unit vector vecS=1/2hati-6/7hatj+1/7hatk . If the flow of solar energy is given by the vector vecF = 910 S in units of watts/mete r^(2) , what is the dot product of vectors vecF with vecN , and the units for this quantity?

Solar Panels have to be installed carefully so that the tilt of the roof, and the direction to the sun, produce the largest possible electrical power in the solar panels. A surveyor uses his instrument to determine the coordinates of the four corners of a roof where solar panels are to be mounted. In the picture , suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters P_(1) (6,8,4) , P_(2) (21,8,4), P_(3) (21,16,10) and P_(4)(6,16,10) What are the components to the two edge vectors defined by vecA = PV of P_(2) - P_(1) and vecB= PV of P_(4) - P_(1) ? (where PV stands for position vector)