In all problems: assume external friction is negligible . a) Two astronauts floa

Question

In all problems: assume external friction is negligible.

a) Two astronauts float in space, at rest relative to each other. The first astronaut, mass M1 = 69.2 kg, holds a ball of mass m = 5.77 kg, which she throws at speed v = 7.86 m/s. The second astronaut, mass M2 = 96.9 kg, then catches the ball. Find vrel, the speed one astronaut is moving relative to the other after one throw and one catch.
1 m/s

b) A machine gun fires bullets of mass m = 78.7 g at muzzle velocity of magnitude v = 943 m/s. The gunner, holding the machine gun in his hands, can exert an average force of magnitude F = 184 N against the gun. Find n, the maximum number of bullets he can fire per minute.
NOTE: The answer must be a whole number. Since you cannot shoot a fraction of a bullet: truncate (chop off) the decimal, instead of rounding.
2 bullets/minute

c) Joe, standing stationary on a beach, sees a small boat of mass M = 138 kg go by at constant speed V = 11.1 m/s. Tom, a man of mass m = 96.8 kg, stands at rest at the back of the boat. Suddenly Tom begins to run toward the front of the boat at speed vrel = 3.01 m/s relative to the boat. Find the speed of the boat v, relative to Joe, while Tom is running.
3 m/s

Explanation / Answer

Two astronauts float in space, at rest relative to each other. The first astronaut, mass 63.4 kg, holds a ball of mass 7.28 kg, which she throws at speed 6.17 m/s. The second astronaut, mass 83.1 kg, then catches the ball. Find the speed one astronaut is moving relative to the other after one throw and one catch. P = mv M1V1 + M2V2 = M1Vf + M2Vf I found the momentum of the first astronaut throwing the ball which is: 7.28(6.12) = 63.4 vf 7.28(6.12)/63.4 = vf -.7027 m/s = vf Also the momentum of the second astronaut catching the ball: 83.1(0) + 7.28(6.17)/ 83.1 + 7.28 = vf .497 m/s = vf but im rather confused about what its asking for. It asking for the speed one astronaut is moving relative to the other. Does it matter which astronaut's speed I use or do I need to use a relative velocity equation? If I need to use a relative velocity equation would it be something like: V astro b relative to a = V astro a relative to b + V of astro A and B You probably don't want to write 6.12 when the problem statement says 6.17. I get v=-0.7085m/s for the first astronaut. For the second astronaut your numbers don't add up at all. But to answer your question the relative velocity of the two is the difference between the two velocities if you keep the sign straight. (m_1+m_2)v_i = m_1v_1_f+m_2v_2_f , where I don't quite get the same answer as you for the first astronomer's velocity. And then if you calculate the second astronomer's velocity, you get an answer which is consistent with what you got. Then the relative velocity of astronaut B to astronaut A =vB-vA , where vA is a negative number, therefore v_B_t_o_A=v_B+|v_A|

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