An astronaut with mass M in space has a spring-loaded pellet gun. It fires pelle
ID: 1429279 • Letter: A
Question
An astronaut with mass M in space has a spring-loaded pellet gun. It fires pellets of mass m, giving them a muzzle velocity of vp. He wants to use it to get back to his ship, which he is some distance away from. He only has 2 pellets. He loads the gun points it directly away from the ship, fires a pellet, then loads the next and fires it again. Initially, his velocity relative to the ship is 0 m/s. Find an expression for his speed in terms of m, M, and vp relative to the ship after firing both pellets.
Explanation / Answer
for 1st time.
initial momentum is zero.
and after firing bullet is moving with Vp in opposite direction.
0 = m * -Vp + Mv
v = m Vp / M
for 2nd time.
initial speed of astronaut = v = m Vp/ M
initial speed of bullet = 0
final speed of bullet (wrt to ship) = vp -v = (vp - mvP / M) = Vp ( M - m) / M
using momentum conservation,
M x m VP / M +mx 0 = - m ( Vp ( M - m) / M ) + Mv
(m M Vp + m M Vp - m^2 VP / M ) = Mv
v = 2 m MVp/M^2 - m^2 Vp/M^2 = mVp ( 2M - m ) /M^2