Consider a plane wave that is a superposition of two independent orthogonal plane waves that can be written as the real part of \vec{E} = E_1\exp\left[i\left(kz-\omega t\right)\right]\hat{i} + E_1 \exp\left[i\left(kz-\omega t + \pi\right)\right]\hat{j}E → = E 1 exp ⁡ [ i ( k z − ω t ) ] i ^ + E 1 exp ⁡ [ i ( k z − ω t + π ) ] j ^ where LaTeX: k,\,\omega,\,E_1,\textrm{ and }E_2k , ω , E 1 , and E 2 are all real. If E_1 = E_2, the tip of the electric field vector will describe a trajectory that, as viewed along the z-axis from positive z and looking toward the origin, is a

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

Samir watches a 100-minute movie on his spaceship. maria's spaceshipe flies in the same direction as samir's spaceship but she observes his move to last 125 minutes and his spaceship to be 40 m long. how long does samir observe his own spaceship to be? according to an observer on earth, planet x is stationary. maria and samir depart earth on their spaceships at the same time, each flying at 0.5c. maria flies toward planet x and samir flies in the opposite direction. according to maria, her voyage to planet x takes 9 years. how many years does marias voyage take according to samir?

How to calculate voltage drop in a series circuit