Calculating Power of a Solar Panel

[eehelp]

Homework Statement

If at some particular place and time the sun light is incident on the surface of the Earth along
a direction defined by the unitary vector – vˆ , where vˆ =(4, 3, 5)/sqrt (50) and with a power
density P, what is the total power captured by a solar panel of 1.4 m2
and with an efficiency
of 12% which is oriented along the vector wˆ =(0, 1, 4) /sqrt(17) ?

Homework Equations

The dot/scalar product equation.

The Attempt at a Solution

I took the scalar product of -v and w, this gave me -23/sqrt(50*17), then multiply this by P*1.4*0.12, but my question is that the overall answer I get is negative due to the dot product. Is this possible as total power ? and am I doing this correctly ?.

 

[Doc Al]

which is oriented along the vector wˆ =(0, 1, 4) /sqrt(17) ?

You want the component of sun light going into that panel, so you'd better use the dot product of $-\hat{v}$ and $-\hat{w}$.

 

[eehelp]

Thank you for the reply.
I think I am understanding what you are trying to say. So does it mean that -v points downwards going into the panel ? and it says the panel is orientated along w so I don't understand where does the into bit come from ? I taught if I take -w it would just mean now the panel is in the opposite direction. Unless orientated along w means the vector w is pointing upwards from the panel ?

 

[Doc Al]

Unless orientated along w means the vector w is pointing upwards from the panel ?

That's exactly what it means. The orientation of a plane is typically specified by a vector normal to the plane pointing out of the plane.

 

[HalfLostAndSearching]

Your approach is correct, but the negative sign in front of the dot product indicates that the solar panel is facing in the opposite direction of the sun's rays. This means that the power captured by the solar panel will be negative, which does not make sense physically. In order to get a positive value, you can either change the direction of the solar panel to face in the same direction as the sun's rays, or you can take the absolute value of the dot product. This will give you the total power captured by the solar panel in the given conditions.