You are deep in outer space (far from any gravitational sources) and standing at the center of a rotating platform (it lies in the plane z=0, and rotates ccw with angular velocity 2). you look down and see a puck on the platform with coordinates (x, y) (in your, the tt, frame). a) write down newton's 2nd law for the x & y coordinates of the puck as you observe it (2 eqs) b) write down the general solution to these two equations by changing to complex coordinates (i. e. write n = x + iy) and guessing that one of the solutions has the form n = e-iat (what is the form of the second solution, when you have two solutions which have the same form? this arose in taylor's discussion of the critically damped oscillator in section 5.4) c) at time t=0 the puck is launced from position to = (x0,0) with velocity v = (vxo, vyo) (all in your frame). show that the time dependent coordinates obey: x(t) = (xo + vxot) cos(at) + (vyo + nx)t sin(nt) y(t) = -(xo + vxot) sin(t) + (vvo + 1x)t cos(at)

An charge with mass m and charge q is emitted from the origin, (x,y)=(0,0). a large, flat screen is located at x=l. there is a target on the screen at y position y(h), where y(h) > 0. in this problem, you will examine two different ways that the charge might hit the target. ignore gravity in this problem. 1.assume that the charge is emitted with velocity v(0) in the positive x direction. between the origin and the screen, the charge travels through a constant electric field pointing in the positive y direction. what should the magnitude e of the electric field be if the charge is to hit the target on the screen? express your answer in terms of m, q, y(h), v(0), and l. 2.now assume that the charge is emitted with velocity v(0) in the positive y direction. between the origin and the screen, the charge travels through a constant electric field pointing in the positive x direction. what should the magnitude e of the electric field be if the charge is to hit the target on the screen? express your answer in terms of m, q, y(h), v(0), and l.