Electromanegtic theory time: 3 hours final exam 2017-2018 msc students a. given the vector field a 5yl-5xj +5zk verify stoke's theorm for the hemispherical surface x +y +z2- a b. find the value of v. m if m a( ) - z 20. (.0) ( a(2cos 2p) at is a function of u and u is a function of x, y,z, then show that vo acore + a (a'sine r c if 2 a. for an electric field e = 4r3a, in spherical coodinates. verify the divergence theorem for a sphere of radius r 2. b. transform the vector d 2ya, -2x

Emmy kicks a soccer ball up at an angle of 45° over a level field. she watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. consider only the time that the ball is in the air, after being kicked but before landing. take "north" and "up" as the positive ‑ and ‑directions, respectively, and use ≈10 m/s2 for the downward acceleration due to gravity.