3. a solid sphere is rolling without slipping along a horizontal surface with a speed of 5.50
m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal. what is the
speed of the sphere after it has rolled 3.00 m up the ramp? notice the sphere rises a
height h as it rolls up the ramp.
wf
v
3.00 m
a) 4.01 m/s
b) 8.02 m/s
c) 1.91 m/s
d) 2.16 m/s
e) 3.53 m/s
250

Wo small variable-thrust jets are actuated to keep the spacecraft angular velocity about the z-axis constant at ? 0 = 1.16 rad/s as the two telescoping booms are extended from r1 = 1.18 m to r2 = 4.69 m at a constant rate over a period of 124 seconds. the small 19-kg experiment modules at the ends of the booms may be treated as particles, and the mass of the rigid booms is negligible. determine the necessary thrust t for each jet as a function of time where t = 0 is the time when the telescoping action is begun. after you have the general expression for t, answer the questions. show work.