Acar drives on a curved road that goes down a hill. the car's position is defined by the position vector, r={−[30.0cos(π10.0t)]i+[30.0sin(π10 .0t)]j−(azt)k} ftwhere az=11.0ft/s. the image below shows the system projected onto the x–y plane. what is the magnitude, v, of the car's velocity, v, at t = 5.00 s in ft/s

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.

Assuming compressible flow of air and that the measurements are done at flagstaff a pitot static tube that gives the difference of total and static pressure measures 0.35 m of mercury. what is the velocity of air? assume the temperature to be 300k. (submit your excel or matlab calculation sheet)

Which of the following ziegler nichols tuning methods the response of the controller to a step input should exhibit an s-shaped curve? a)-open loop mode b)-closed loop mode c)-both modes (open & closed) d)-none of the modes (open & closed)