An astronaut with a mass of #75 kg# is floating in space. If the astronaut throws an object with a mass of #35 kg# at a speed of #5/6 m/s#, how much will his speed change by?

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Answer 1 · 2016-11-22T23:34:42

Suppose before throwing the object the astronaut has speed #u#, and afterwards has speed #v# #ms^-2#

Before:

# {"astronaut (75) and object (35)"} rarr u #

After;

# { "astronaut (75)" } rarr v #
# { "object (35)" } rarr 5/6 #

By the Conservation of Linear Momentum:

# (75+35)(u) = (75)(v) + (35)(5/6) #
# :. 110u = 75v + 175/6 #
# :. 75v = 110u -175/6 #
# :. v = 22/15u - 7/18 #