Three objects lie in the x, y plane. each rotates about the z axis with an angular speed of 5.58 rad/s. the mass m of each object and its perpendicular distance r from the z axis are as follows: (1) m1 = 5.46 kg and r1 = 1.98 m, (2) m2 = 3.64 kg and r2 = 16.50 m, (3) m3 = 3.21 kg and r3 = 3.09 m.

(a) find the tangential speed of each object.
(b) determine the total kinetic energy of this system using the expression ke =

Afaulty model rocket moves in the xy-plane (the positive y direction is vertically upward). the rocket's acceleration has components ax(t) = ? t2 and ay(t) = ? ? ? t, where ? = 2.50 m/s4 , ? = 9.00 m/s2 , and ? = 1.40 m/s3 . at t = 0 the rocket is at the origin and has velocity ~v0 = v0x ? i + v0y ? j with v0x = 1.00 m/s and v0y = 7.00 m/s. (a) calculate the velocity and position vectors as functions of time. (b) what is the maximum height reached by the rocket? (c) sketch the path of the rocket. (d) what is the horizontal displacement of the rocket when it returns to y = 0?