1) an astronaut at rest in space fires a thruster pistol...?

Question

that expels 35 g of hot gass at 875 m/s. the combined mass of the astronaut and pistol is 84 kg. how fast and in what direction is the astronaut moving after firing the pistol?

2) a 2 kg ball, a is moving at a speed of 5 m/s. it collides with a stationary ball, b of the same mass. after the collision, a moves off in a direction 30 degrees to the left of its original direction. ball b moves off in a direction 90 degrees to the right of ball a's final direction. how fast are they moving after the collision?

Answer 1

1. Conservation of momentum
m1V1=m2V2 then
V2=m1V1/m2=
V2= .035 x 875/84=0.365m/s

2.Again we have conservation of momentum
since m1=m2
mV1=mu1 + mu2 (vector equation)
with one ball 30 degrees to the left ( or 120 degrees) and the other (120 - 90=30) 30 degrees.
Sketch the diagram to better visualize.

X- components
0= -m u1cos(60) + mu2cos(30)
u2cos(30)= u1cos(60)
u2= u1cos(60)/cos(30)

Y- components
mv1=mu1sin(60) + mu2sin(30)

v1=u1sin(60) + u1(cos(60)/cos(30))sin(30)
u1= v1/[sin(60) + (cos(60)/cos(30))sin(30)]

Now just compute the values of u1 first and then u2.

Have fun