1) A 60 kg boy and a 40 kg girl, both wearing skates face each other at rest on

Question

1) A 60 kg boy and a 40 kg girl, both wearing skates face each other at rest on a frictionless ice surface.  The boy then pushes the girl away, sending her eastward with a speed of 4.0 m/s.  What is the resulting speed and direction of the boy?.

2) The mass of the moon is 0.0123 times the mass of the earth. The distance between the moon and the earth as measured from their centers is about 3.84 x 108 m. Determine the location of the center of mass of the earth-moon system as measured from the center of the earth.

3) A rocket which has an exhaust speed of 8.0 km/s is to have a lift-off vertical acceleration of 8.0 m/s2 from the NASA launch pad.  If the initial mass of the rocket is 6.0 x 106 kg, at what minimum rate must the rocket consume fuel?

Explanation / Answer

mass m1= 60 kg

m2 = 40 kg

from conservation momentum

m1u1+m2u2 = m1v1+m2v2

initially both are at rest

so u1=0 , u2= 0

and v2 = 4 m/s

==> 0 = 60v1 + 40(4)

==> v1=-160/60 = -2.666 m/s

negative sign shows direction is westward

2)

Mmoon = 0.0123 Mearth

distance r =3.84x10^8 m

==> Rcm = 0.0123*Me*3.84x10^8/(Me+0.0123Me) = 4.66 x 10^6 m from earth

3)

thrust = dm/dt *v

==> m(g+a) = dm/t*v

==> dm/dt = m(g+a)/v = 6x10^6 x (9.8+8)/8000 = 13350 kg/s = 1.335 x 10^4 kg/s

option C

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