An astronaut of mass 84.0 kg is taking a space walk to work on
the International Space Station. Because of a malfunction with the
booster rockets on his spacesuit, he finds himself drifting away
from the station with a constant speed of 0.550 m/s. With the
booster rockets no longer working, the only way for him to return
to the station is to throw the 7.65 kg wrench he is holding.
In which direction should he throw the wrench?
away from the stationtoward the station
He throws the wrench with speed 16.47 m/s WITH RESPECT TO HIMSELF.
(Hint: That is NOT the speed an observer on the space station would
see. Think of a traveler walking on a moving walkway at the
airport. The velocity of the traveler with respect to the ground
equals the velocity of the traveler with respect to the moving
walkway plus the velocity of the moving walkway with respect to the
ground. For this problem, the velocity of the wrench with respect
to the space station equals the velocity of the wrench with respect
to the astronaut plus the FINAL velocity of the astronaut with
respect to the space station.)
After he throws the wrench, how fast is the astronaut drifting
toward the space station?
What is the speed of the wrench with respect to the space
station?
a) away from the station
b) let v is the speed of astronaut towards the space station.
let M = 84 kg
m = 7.65 kg
Apply conservation of momentum
initial momentum = final momentum
(m + M)*0.55 = m*(0.55 + 16.47) + M*v
(7.65 + 84)*0.55 = 7.65*(0.55 + 16.47) + 84*v
==> 84*v = (7.65 + 84)*0.55 - 7.65*(0.55 + 16.47)
= -79.8
v = -79.8/84
= -0.95 m/s
speed, |v| = 0.95 m/s <<<<<<-----Answer
speed of wrench with respect to space station = 0.55 + 16.47
= 17.02 m/s <<<<<<-----Answer
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