An astronaut with a mass of #95 kg# is floating in space. If the astronaut throws an object with a mass of #4 kg# at a speed of #1/8 m/s#, how much will his speed change by?

Question

An astronaut with a mass of #95 kg# is floating in space.  If the astronaut throws an object with a mass of #4 kg# at a speed of #1/8 m/s#, how much will his speed change by?

Amelia Adams · Accepted Answer

This examines momentum conservation. It is assumed that there is no air resistance and no gravity because the astronaut is floating in space, so you should move backward when you toss an object forward. Newton's Third Law states that an object will push you back if you push it. Since the astronaut and the object are moving in different directions, if the object is thrown to the right, we have conservation of momentum in the following way: #Deltap_o - Deltap_a = 0# #vecp_(o,i) - vecp_(o,f) = vecp_(a,i) - vecp_(a,f)# #vecp_(o,i) - vecp_(a,i) = vecp_(o,f) - vecp_(a,f)# #cancel(m_(o,i)vecv_(o,i)) - cancel(m_(a,i)vecv_(a,i)) = m_(o,f)vecv_(o,f) - m_(a,f)vecv_(a,f)# where #o# is object, #a# is astronaut, and #i# and #f# are initial and final, respectively. Both the astronaut and the object start at rest, so initial momenta are #0#, and we've defined rightwards motion as positive. Consequently: #m_(a,f)vecv_(a,f) = m_(o,f)vecv_(o,f)# #v_(a,f) = |(m_(o,f)v_(o,f))/(m_(a,f))|# #color(blue)(v_(a,f)) = (("4 kg")("0.125 m/s"))/(("95 kg"))# #color(blue)"= 0.0053 m/s"#
in the opposite direction. The astronaut's new speed is represented by the change in speed, assuming that he began at rest.

Emily Abbate · Answer

undefined To find the change in the astronaut's speed, you can use the principle of conservation of momentum. The change in momentum of the astronaut and the object will be equal and opposite. Calculate the initial momentum of the astronaut and the object, then calculate the final momentum after the object is thrown. Finally, use the equation Δp = mΔv to find the change in velocity of the astronaut.