1.anobjectstartsfallingtowardthecenteroftheearthattheinitialdistancer1(totheearth'scenter).intermsofr1,theearth'smassmandgravitationconstantG,writethespeedfunctionv=v(r).thevariableristhedistancetothecenteroft

Question

1.an object starts falling toward the center of the earth at the initial distance r1(to the earth's center).in terms of r1,the earth's mass m and gravitation constant G,write the speed function v=v(r).the variable r is the distance to the center of the earth.(r1>r>R,R is the earth's radius)
2.A 1000kg boat is traveling at 90km/h when its engine is shut off.the magnitude of the friction force between boat and water is proportional to the speed v:f= -70v,where v is in m/s and f is in N.find the time required for the boat to slow to 46km/h

Answer 1

Second Q:
Use:force = mass x acceleration
-70v = 1000(dv/dt)
hence,dv/v = -(70/1000)dt
integrate on both sides with v from 90 km/h to 45 km/h,and t from 0 to t
ln(45/90) = -(70/1000)t
i.e.t = (1/0.07).ln(90/45) s = 9.9 s