A farmer uses a conveyor belt to move grain from ground level into a storage silo. The conveyor has a length of 9 metres. Its angle of elevation can be adjusted from 5° to 20°. The silo has an opening that can accommodate the conveyor belt at its lowest and highest settings. Determine the size of the opening of the silo, to the nearest tenth of a metre.

Answer 1

Assuming zero thickness for the belt, grain and accompanying hardware, the height of the top of the opening is

hi = 9*sin20° = 3.078m

So, the height at 5° is lo = 9*sin5° = 0.784m

hi-lo = 2.294m