In the figure particles 2 and 4, of charge -e, are fixed in place on a y axis, at y2 = -8.48 cm and y4 = 4.24 cm. Particles 1 and 3, of charge +e, can be moved along the x axis. Particle 5, of charge +e, is fixed at the origin. Initially particle 1 is at x1 = -8.48 cm and particle 3 is at x3 = 8.48 cm. (a) To what x value must particle 1 be moved to rotate the direction of the net electric force on particle 5 by 30 degrees counterclockwise?
(b) With particle 1 fixed at its new position, to what x value must you move particle 3 to rotate back to its original direction?

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.