In the nuclear industry, workers use a rule of thumb that the radioactivity from any sample will be relatively harmless after 10 half-lives. Calculate the fraction of radioactive sample that remains after this time period. What does this mean for the Rocky Flats cleanup operation, which occurred at the former Rocky Flats Plant just outside of Boulder that generated plutonium triggers for nuclear weapons ( 239 Pu decay rate

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?