Two arrows are shot vertically upward. The second arrow is shot after the first one, but while the first is still on its way up. the initial speeds are such that both arrows reach their maximum heights at the same instant, although these heights are different. Suppose the that initial speed of the first arrow is 41 m/s and that the second arrow is fired 0.306122448979592 seconds after the first. Determine the maximum height of arrow 1 in meters.

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

To understand the electric potential and electric field of a point charge in three dimensions consider a positive point charge q, located at the origin of three-dimensional space. throughout this problem, use k in place of 14? ? 0. part adue to symmetry, the electric field of a point charge at the origin must point from the origin. answer in one word. part bfind e(r), the magnitude of the electric field at distance r from the point charge q. express your answer in terms of r, k, and q. part cfind v(r), the electric potential at distance rfrom the point charge q. express your answer in terms of r, k, and q part dwhich of the following is the correct relationship between the magnitude of a radial electric field and its associated electric potential ? more than one answer may be correct for the particular case of a point charge at the origin, but you should choose the correct general relationship. a)e(r)=dv(r)drb)e(r)=v(r)rc)e(r)=? dv(r)drd)e(r)=? v(r)r

Four objects each with charge +2.0×10−7c are located at the corners of a square whose sides are 2.0 m long. part a what quantities can be determined using this information? check all that apply. the electric force on a charged object placed at the center of the square. the mass of each object. the total electric potential energy of the system consisting of the four charged objects. part b find the electric force on a charged object placed at the center of the square.