Consider a series combination of a 1mH inductor and a 27Ω resistor, which we can think of as a circuit model of a motor. Further, assume that the power company operates at a frequency of 5KHz (to keep our capacitor values reasonable compensating a real motor at 60Hz would follow an identical procedure)

a. If the voltage supplied by the power company is V020°, determine the complex power supplied to the series load (in terms of Vo), the power factor, and the power factor angle:
PF =
b. Determine the value of a shunt capacitor to eliminate the reactive power drawn by the overall load, as seen by the power company. What is the power factor of the new overall load? Create a combination of (<= 3) capacitors from your kit to closely match the required compensation capacitor. PF =

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.