4. (this is a 10 point problem) (a) Draw a right triangle with acute angle = /6 , whose opposite leg has length y. What is the length of the hypotenuse?

(b) Consider a 2 meters wide by 3 meters tall rectangle sheet of metal that is submerged in water ( = 1000 kg/m3 ) so that the sheet's width is oriented horizontally and the sheet itself is tilted at = /6 radians above the horizontal. The highest point of the sheet just grazes the top of the water.

i. Draw a picture, and label the variable y to represent the depth of the water in meters. What is the interval for the y values that we are concerned with if we want to compute the fluid force on one side of the metal sheet?

ii. We want to compute the fluid force on one side of the sheet of metal. We can compute the force by adding up approximations of horizontal slices of the rectangular sheet. For each infinitesimal slice, what is the width and "height"? Hint: the height is NOT y.

(c) Repeat the (a),(b),(i), and (ii) for = /4 .