Consider the following descriptions of the vertical motion of an object subject only to the acceleration due to gravity. Begin with the acceleration equation att) :v'(t) : Q. where g : 7 9.8 mfsz. a. Find the velocity at the object for all relevant times. In. Find the position of the object for all relevant times. 0. Find the time when the object reaches its highest point. what is the height? d. Find the time when the object strikes the ground. A softball is popped up vertically (from the ground) with a velocity o133 m/s. a. v(t) = a. A rectangular pen is built with one side against a barn. If 1000 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of the pen? b. A rancher plans to make four identical and adjacent rectangular pens against a barn, each with an area of 25 m (see figure). What are the dimensions of each pen that minimize Barn the amount of fence that must be used? 25 25 25 25 a. To maximize the area of the pen, the sides perpendicular to the barn should be m long and the side parallel to the barn should be m long. (Type exact answers, using radicals as needed.)A rectangular tank with a square base, an open top, and a volume of 2,048 fto is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. The tank with the minimum surface area has a height of it and a square base with a side length of |ft.Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width, and height not exceeding 78 in. What are the dimensions and volume of a square-based box with the greatest volume under these conditions? The length of the square-end edge is in. The box height is in