5.1 A reference frame xyz is moving such that the origin O has at time t a velocity relative to reference XYZ given as V, 6i+12j+13k m/s the xyz reference has an angular velocity to relative to XYZ at time t given as 10+12j+2k rad/s. What is the time rate of change relative to XYZ of a directed line segment p going from position P (3.2,-5) to Q (-2.4.6) in xyz ? What is the time rate of change relative to XYZ of position vectors i' and k'? 5.2 A reference xyz is moving relative to XYZ with a velocity of the origin given at time t as V.=6i + 4j + 6k m/s. The angular velocity of reference xyz relative to XYZ is w=3i+14j+2k rad/s. What is the time rate of change as seen from XYZ of a directed line segment p1.2 in xyz going from position I to position 2 where the position vectors in xyz for these points are, respectively pi= 2i+3j' m. p= 31'-4j+2k m. Ans. -1060i +7.31j-35.2k m/s Prob.5.1 J 30° 3% 30% это Elevation. Prob 52 85 Plan Prob.5.4.5.5.5.12 5.3 Find the second derivative as seen from XYZ of the vector P1.2 specified in Problem 5.2. Take the angular acceleration of xyz relative to XYZ at the instant of interest as a 15i-2k rad/s². Ans. - 521i+108.7j+65.2k m/s². 5.4 A tank is maneuvering its gun into position. At the instant of interest, the turret A is rotating at an angular speed 0 of 2 rad/s relative to the tank and is in position 0-20°. Also, at this instant, the gun is rotating at an angular speed of 1 rad/s relative to the turret and forms an angle -30° with the horizontal plane. What are, (ang.accn.) of the gun relative to the ground? Ans. -3.76i -1368j 5.5 In Problem 5.4 determine and assuming that the tank is also rotating about the vertical axis at a rate of 0.2 rad/s relative to the ground in a clockwise direction as viewed from above. Ans. 0.941i+0.342j+1.8k rad/s, 1.692j-0.616i rad/s². 5.6 A cord is wrapped around a wheel which is initially at rest as shown. If the end A of the cord is given acceleration a 4t m/s² where t is in seconds, find, as a function of time (a) the angular velocity of the wheel, and (b) the angular position of line OP in radians. (Line OP is on the wheels). Ans. 10t² rad/s, 3.33 t'rad 5.7 Disc A. shown in fig. starts from rest and rotates with a constant ang. Acceleration of 2 rad/s². If disk A is in contact with disc B and no slipping occurs between the discs, compute the angular velocity and angular