# Thread: Amount of sun falling on a lake

1. ## Amount of sun falling on a lake

The amount of sunlight falling on each unit of area of a horizontal surface(such as a lake)-which is known as "insolation"- depends on the height of the sun in the sky. It is not unreasonable to suppose that, with t measured in hours from sunrise, d denoting the total hours of daylight, and m the elevation of the sun at noon, the insolation function is given by sin(m)sin((pi*t)/d). Find the average amount of insolation over the course of daylight hours.

I don't even know where to start so if you have any ideas please let me know

2. Originally Posted by Alice96
The amount of sunlight falling on each unit of area of a horizontal surface(such as a lake)-which is known as "insolation"- depends on the height of the sun in the sky. It is not unreasonable to suppose that, with t measured in hours from sunrise, d denoting the total hours of daylight, and m the elevation of the sun at noon, the insolation function is given by sin(m)sin((pi*t)/d). Find the average amount of insolation over the course of daylight hours.

I don't even know where to start so if you have any ideas please let me know
average value of a time dependent function ...

$\frac{1}{t_f-t_0} \int_{t_0}^{t_f} f(t) \, dt$