Arectangular key was used in a pulley connected to a line shaft with a power of 7.46 kw at a speed of 1200 rpm. if the shearing stress of the shaft and key are 30 mpa and 240 mpa, respectively what is the length of the rectangular key if the width is one fourth that of the shaft diameter?

Arunner is training for an upcoming marathon by running around a 100-m-diameter circular track at constant speed. let a coordinate system have its origin at the center of the circle with the x-axis pointing east and the y-axis north. the runner starts at (x, y) = (50 m, 0 m) and runs 2.5 times around the track in a clockwise direction.