The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region above the curve y = 0.1x² and below the line y = 160. (Here, distances are measured in meters.) The water level is 26 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by kg water pressure. (Water has a density of 1000- and the acceleration of gravity is 9.8- m m³ sec²

The drag force, Fp, acting on an immersed body by a moving fluid can be calculated as PU? 2 where C, is the drag coefficient, A is the projected area of the body on a plane normal to the Fp = CpA flow, p is the mass density of the fluid, and U is the undisturbed velocity of the fluid. Suppose Cp, A, and p are known constants of values 0.6, 10 ft2, and 1.94 slug/ft, respec- tively. U is a lognormal random variable with parameters hy and Sy. Determine the distribution of Fp-

1. A ball is thrown up in the air from a cliff with the initial speed of 10 meters per second and hits the ground 11 seconds later. How tall is the cliff? You may assume that the acceleration due to gravity is –10 meters per second squared.

Consider an axisymmetric feeding bowl as shown on the left below. Its cross-section is shown on the right with the axis of symmetry aligned along the y-axis. The top curve of the cross-section is given by the function b. What is the capacity of this bowl? Capacity= cm³ c. Find the volume of water inside the bowl if the water level is 3.3 cm measured from the bottom. Volume of water = 1 961 y = C 961 The horizontal base joins the endpoints of the top curve. Both x and y are in cm. You may need to use a computer algebra system to solve some of the following problems. Round all your answers to at least 3 significant figures. a. Assume that the bowl is solid and is made with plastic. Find the amount of plastic (as a volume) required to make this bowl. Amount of plastic = cm³ cm3 -x4 (9-x) 1 4 -x¹ (9 + x) y 0≤x≤9.1 -9.1 < x < 0 X